121 Q1. If x is continuous variable and follows probability density function x/7; 2<x<4 f(x) =...

Question

Question

Answer 1

Answer #1

Solution x is continuous variable and follows probability density function, f(x)= 817 ; a< < 4 0 ; otherwise 3 P(2< x <3) = s

Answer 2

Similar Homework Help Questions

b. Let X be a continuous random variable with probability density function f(x) = kx2 if...

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()...

(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.
2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4,...

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

2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else...

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.
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451...

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.
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y)...

Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.

1. Let X be a continuous random variable with probability density function f(x) = { if...

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].
2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero...

2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero otherwise. = , Find the probability distribution of Y-g(x)- 12 XI
3. Let X be a continuous random variable with probability density function ax2 + bx f(0)...

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...

The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk....

The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)