So9lve the below:
Q1. Let the random variable X have the p.d.f.
f(x)=2(1-x) for 0
a. Sketch the graph
b. Determine and sketch the graph of the distribution function of X
c. find P(X) for the following intervals: i. [0,1/2] ii. [1/4,3/4] iii. X=3/4 iv. X>3/4
Q2. For each of the following functions (i) find the constant c so that f(x) is a p.d.f of a random variable X, (ii) find the distribution function F(x)=P(X
a. f(x)=(x^3)/4 0b f(x)=3(x^2)/16 -cc. f(x)= c/sqrt(x) 0
Q3. For each of the following functions (i) find the constant c so that f(x) is a p.d.f of a random variable X, (ii) find the distribution function F(x)=P(X
a. f(x)=4x^c 0b. f(x)=c/sqrt(x) 0c. c/(x^3/4) 0