Q 2. The probability density function of the continuous random variable X is given by Shell,...
7.2. Which of the following functions represent a probability density function for a continuous random variable? Hint: Check if both rules of a proper probability density function hold. (a) f(z) = 0.25 where 0-1-8. b) f(r) =1/2 where 0 <1<2
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7, where q = 1- p and 0 < p < 1. Use this to derive the mean and variance of X.
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
Question #37 Let X be a continuous random variable with the following density function: p(-x+ /2) for - 0<x<00. Calculate E[X | X > 0). Possible Answers B 1/727 © 12 D/2TR Ⓡ 1.00