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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?

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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?

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