Q.1 A continuous random variable X has the following function fx (x) = {K -3
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- Example 3: The probability density ƒ(x) of a continuous random variable is given by f(x) 3 ce , -m3 Let X be the number of siblings of WSU students. The pdf of X is: f(x) = (5-x)/15 for x = 0, 1, 2, 3, 4 What is the probability that a randomly selected student has 3 or more siblings if it is known that they are not an only child X 0.133 X 0.2 / 0.3 O X 0.667 X 0.933[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).A random variable has probability density function f(x) = 30x (1 - x) <(0 < xs 1). Compute its cumulative distribution F(x). O 10x3- 15x4 + 6x5 + 1 O 30x(1 - x) O 30x2 - 60x3 + 30x4 O 10x3 - 15x4 + 6x5 O none of these A Moving to the next question prevents changes to this answer. to search 63°F S End F10 Home %23 PrtScn F8 F2 F3 F4 F5 F6 F7 F9 近Q.3 The probability density function for a continuous random variable X is fx(x) = {a + bx²; 0If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (TrụeQ1 (a) Given probability distribution function for discrete random variable X as below: 2 4 8 10 P(X = x) 0.08 0.25 0.35 0.2 0.12 (i) Find the mean of X. (ii) Find the variance of X. (b) Let the continuous random variable X has probability density function as follows, (k(x + 2)², -2Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON