Problem 1. Let X be a contiuous random variable with probability density 2T f0SS Let A...
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.
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
3. (10 pts.) X is a Gaussian random variable with E{X} = 2 and Var(X) = 16. Let Y = 3X +1. Determine the probability: Pr(Y > 2)
Let > 0 and a > 0 be given. Suppose that X is a random variable with moment generating function e My(t) = {(A-ta tsy Top til Compute Var(X). Show that if we define Ly(t) = In My(t) then Ls (0) = Var(X).
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
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. Additional Problem 6. Let X be a continuous random variable with pdf f(x) = (z + 1), -1 x 2. (a) Compute E(X), the mean of X. (b) Compute Var(X), the variance of X (c) Find an expression for Fx(), the edf of X. (d) Calculate P(X > 0). (e) Compute the mean of Y, where Y (f) Find mp, the pth quantile of X X-1 X+1
10. Let X be a continuous random variable with probability density function -T xe h(x) = { x > 0 x < 0 0 a. Verify that h(x) is a valid probability density function. [7] b. Compute the expected value E(X) and variance V(X) of X. [8]
10. Let X be a continuous random variable with probability density function -2 хе x > 0 h(z) = { { 0 x < 0 a. Verify that h(x) is a valid probability density function. [7] b. Compute the expected value E(X) and variance V(X) of X. [8]