# Random Variable

Here are questions 33 and 34 to assist in answering question 52.

33) Let X be a random variable with probability density

f(x)={c(1-x^2), -1<x<1

0 otherwise

(a) What is the value of c?

(b) What is the cumulative distribution function of X?

34) Let the probability density of X be given by

f(x)={c(4x-2x^2), 0<x<2

otherwise

0(this zero is right under the c and is enclosed in the bracket)

(a) What is the value of c?

(b) P{1/2<X<3/2}=?

37) Let X1, X2, ...., Xn be independent random variables, each having a uniform distribution function of M, Fm (.), is given by

Fm(x)=x^n, 0(less than or equal to)x(less than or equal to) 1

What is the probability density function of M?

https://brainmass.com/statistics/probability-density-function/random-variable-3973

#### Solution Summary

Here are questions 33 and 34 to assist in answering question 52.

33) Let X be a random variable with probability density

f(x)={c(1-x^2), -1<x<1

0 otherwise

(a) What is the value of c?

(b) What is the cumulative distribution function of X?

34) Let the probability density of X be given by

f(x)={c(4x-2x^2), 0<x<2

otherwise

0(this zero is right under the c and is enclosed in the bracket)

(a) What is the value of c?

(b) P{1/2<X<3/2}=?

37) Let X1, X2, ...., Xn be independent random variables, each having a uniform distribution function of M, Fm (.), is given by

Fm(x)=x^n, 0(less than or equal to)x(less than or equal to) 1

What is the probability density function of M?