X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)-...
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
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).
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
4. [10 pts] Let X be a random variable with probability density function if 1 < a < 2, 2 f(a)a 0 otherwise. Find E(log X). Note: Throughout this course, log = loge.
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
121 Q1. If x is continuous variable and follows probability density function x/7; 2<x<4 f(x) = then find the value of P(2<x<3) ? 0; otherwise
2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4, zero otherwise. Find the probability distribution of Y-g(X)- XI
x(3-x) 0<x<3 Let X be a continuous random variable with density function What is the mode of X. Answer in simplied fraction form
(6) Suppose that X is an absolutely continuous random variable with density 1<I<2 f(3) = lo, otherwise. Find (a) the moment generating function MX(t). (b) the skewness of X (c) the kurtosis of X (7) Suppose that X, Y and Z are random variables such that p(X,Y) = 1 and p(Y,Z) = -1. What is p(X, Z)? Explain your answer. (8) Suppose that X, Y and Z are random variables such that p(X,Y) = -1 and p(Y,Z) = 0. What...