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QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density function f(x)= 2x 0<x< 1 unction fx)= {** orsak<2 1 o else Find P(X< 0.5) QUESTION 4 1 points Save Answer 2x 0<x< 1 Let X be a continuous random variable with probability density function f(x) = { 10 else Find P(-0.5<x<0.5) QUESTION 5 1 points Save Answer . The cumulative distribution Let X be a continuous random variable with probability density function f(x) = { 2x 0<x<1 lo else function is Fix). Find F(0.5) QUESTION 6 1 points Save Answer 2x 0<x<1 Let X be a continuous random variable with probability density function f(x) = { 10 else unction f(x) = {24 Orsa < 1The cumulative distribution The cumulative distribution function is F(x). Find EX

Answer 1

1:

SL0 = 2 * 5 = [] = 8,5 = 17<x)d

2:

The total area under the probability density curve of a continuous random variable is 1.

3:

P(X < 0,5) = ) 2rdx = [22795 – 0.28

4:

70.5 P(-0.5 < X < 0.5) = P(0 < X < 0.5) = 120dx = [2210.5 = 0.25

5:

The CDF of X is

$F(X)=\int_{0}^{x}f(x)dx=\int_{0}^{1}2xdx=\left [ x^{2} \right ]_{0}^{x}=x^{2}$

F(0.5) = 0.52 = 0.25

6:

E(X) = ['as()de – [*22 de = 1

7:

Now

Ex) - [ 2s(optr - 'zar - 19:21.- AN

Var(X) = E(X) – [E(X)]2 =