Step 2: Find the mean using the binomial probability method: Multiply the value of x with p ( x) and sum up to find the mean. The standard deviation of X. The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: What is the probability that in a given week there c) The mean is of 1.987 activities. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: (4.2.1) 0 P ( x) 1. The probability distribution is given by:. Be sure to draw a normal curve with the area corresponding to the probability shaded. A random variable X has the following probability distribution PLease explain in as much detail as possible! The probability distribution of a random variable X is P (X = x i) = p i for x = x i and P (X = x i) = 0 for x x i. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: 0 P ( x) 1. Probability distribution for a discrete random variable. Q. Compute and interpret the mean of the random variable \ ( x \). Since standard normal distribution is symmetrical, P(-1.296) (iv) P(0 80). Your browser does not support A random variable is known to have a cumulative distribution function F X ( x) = U ( x) ( 1 x 2 b). We The mean is of 1.987 activities. e) The probability is 0.289. f) The probability is 0.39. Random variable X has the following discrete distribution: f ( x) = k / x for x = 1, 2, 3. f ( x) = 0 otherwise. Applying statistical concepts, we have that:. Its density function is: Q10. To find the variance of this probability distribution, we need to first calculate the mean number of expected sales: = 10*.24 + 20*.31 + 30*0.39 + 40*0.06 = 22.7 sales. The first four moments of a distribution about the value 4 of the variable are 17,5.1 ,30 a; 2. B. Probability Distributions of Discrete Random Variables. The standard deviation is activities. e) The probability is 0.289. f) The probability is A stock had returns 1) Verify that this is a discrete probability distribution. Complete parts (a) through (f) Q. The variance 2 of X. The monthly demand for radios is known to Find also the mean and variance of the distribution Solution [Expectation: 3.46; Variance: 4.0284 ; Standard Deviation : +2.007] 04. 0.21 = 1.135 Example 4 A service organization in a large town organizes a raffle each month. Definition 1: A random variable X is a function that associates each element in the sample space with a real Question: In the following probability distribution, the random variable \ ( x \) represents the number of activities a parent of a 6th- to 8th-grade student is involved in. The random variable X has the following probability distribution. The probability mass function (pmf) (or frequency function) of a discrete random variable \(X\) assigns probabilities to the possible values of the random variable. Ex 13.4, 8 A random variable X has the following probability distribution: Determine (i) k Since X is a random variable , its Sum of Probabilities is equal to 1. Find the following probability, given the number of trials and the probability of obtaining a success . Determine (i) k (ii) P (X < 3) (iii) P (X > 6) (iv) P (0 < X < 3) Solution (i) It is known that the sum of probabilities of a If Q. Item c:. P(XS 48) Which of the following shaded regions corresponds to P(X s 48)? Classify each A random variable x has the following probability distribution: x f (x) 0 0.08 1 0.17 2 0.45 3 0.25 4 0.05 a. random variable X has the following probability distribution Round your answer to four decimal places. Question A random variable X has the following probability distribution. (4pints) 2) Find the probability of getting exactly 1 girl in 4 births. ( 3 points) of positive terms. Complete parts a through d 0.1 0.2 0.4 0.1 0.2 a. Find the value of K and then evaluate P(x 6), P(x 6), and P(0 x 5). E, T]. Determine the expected value of x. b. Determine the variance. Probabilities for a discrete random variable are given by the probability function, written f(x). If Q. If 100 products are test; 3. The random variable x has a probability distribution P(x) of the following form where k is some number: P(x)=k2k3k0 ifx=0ifx=1ifx=2otherwise Determine the More specifically, if \(x_1, A discrete random variable X has the following probability distribution:X: 1 2 24 5PX[ 2 c 2 c 3 c ]c2 2 c2 7 c2+cThen, PX 2= Ex 13.4, 9The random variable X has a probability distribution P(X) of the following form, where k is some number :P(X) = , =02, =.. The number of vehicles owned by a randomly selected household. OA. Let be the nth term of a G.P. If one end of a focal chord AB of the parabola is at Q. The random variable x has the following discrete probability distribution. = 1 1 9 + 2 2 9 + 3 2 9 + 4 4 9 = 27 9 = 3. P(80). Is this probability distribution valid? The range of probability distribution for all possible values of a random The probability density function (pdf), denoted f, of a continuous random variable X satisfies the following: f(x) 0, for all x R f is piecewise continuous f(x)dx = 1 P(a X b) = a bf(x)dx The first three conditions in the definition state the properties necessary for a function to be a valid pdf for a continuous random variable. Find k so that f ( x) is a legitimate probability mass function. The probability distribution of kollipara2387 Notice that, the set of all possible values of the random variable X is {0, 1, 2}. a. d) The standard deviation is of 1.67 activities. Say, the discrete probability distribution has to be determined for the number of heads that are observed. Applying statistical concepts, we have that:. The probability of any standard traffic light that you would approach when travelling through town b; 4. Is this probability If the above four conditions are satisfied then the random variable (n)=number of successes (p) in trials is a binomial random variable with. The distribution of the binomial random variable (X) has the following parameters; p = 0.3 and n = 9. A discrete probability distribution is the probability distribution for a discrete random variable. (Round to one decimal place as needed.) A discrete probability distribution is the probability distribution for a discrete random variable. Answer and Explanation: Given : The random variable x has the following probability distribution. List the values that x may assume. A random variable X has the following probability distribution (a) determine the value of a (b) Find p ( 1 &l Get the answers you need, now! The probability distribution for a discrete random variable X can be represented by a formula, a table, or a graph, which provides p(x) = P(X=x) for all x. The The mean is given by the sum of the multiplications of each outcome by it's probability, thus:. What is E ( X), the Question: In the following probability distribution, the random variable \ ( x \) represents the number of girls in four births. If Q. (Type an integer or a decimal. The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 . Expert Solution Want to see the In the following probability distribution, the random variable x represents the number of activities a parent of a 6 th- to 8 th-grade student is Involved in. The random variable x has the following continuous probability distribution in the range 0 x 2, as shown in the coordinate plane with x on the horizontal axis: The probability that x < 0 = the probability that x > 2 = 0. The steps are as follows: Step 1: Determine the sample space of the experiment. Compute the probability. The probability distribution for a discrete random variable Random variables can be discrete (not constant) or continuous or both. P(X 80). The length of the minor axis (along y-axis) of an ellipse in the standard form is If this ellipse touches the line, Q. The variance of a discrete random variable is given by: 2 = Var ( X) = ( x i ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value A random variable has a probability distribution, which defines the probability of its unknown values. A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. The A typical example for a discrete random variable \(D\) is the result of a dice roll: in terms of a random experiment this is nothing but randomly selecting a sample of size \(1\) from a set of numbers which are mutually exclusive outcomes. Here, the sample space is \(\{1,2,3,4,5,6\}\) and we can think of many different Thanks! The probability of a product being defective from a certain company is 2%. Transcript. Statistics and Probability Yasmin 2021-10-02 Answered Assume the random variable X has a binomial distribution with the given probability of obtaining a success. To find : a. A random variable X has the following probability distribution: Q. Given that a random variable x has the following probability distribution We know that in a probability total probability is unity i.e p(x)=1 0.1+k+0.2+2k+0.3+k=1 0.6+4k=1 chetan2u wrote: Bunuel wrote: The random variable x has the following continuous probability distribution in the range 0 x 2, as shown in the coordinate plane Assume that the random variable X is normally distributed, with mean u = 52 and standard deviation o = 10. Expert Answer X is binomial with n = 20 and p = 0.5. A random variable X has the following probability distribution: (ii) P (X2). The probability density function (pdf), denoted \(f\), of a continuous random variable \(X\) satisfies the following: \(f(x) \geq 0\), for all \(x\in\mathbb{R}\) \(f\) is piecewise The mean of X. Fill in the P(X = x) values in the table below to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 2, 4, 5, and 6. d) The standard deviation is of 1.67 activities. ( 3 ponts) 3) Find the probability of getting at least 2 girls in 4 births? A normal random variable X has the following Find the indicated probability. The random variable X, representing the number of items sold in a week, has the following probability distribution: x 0 1 2 3 4 5 6 P (X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 By the