Consider the function f : R® — R defined by0 zcx 0T@=1 cs-2) 150 x 3where c is an undetermined...

Question

Consider the function f : R® — R defined by
0 z<0
cx 0T@=1 cs-2) 150 x >3
where c is an undetermined constant.
(a) For what value of ¢ is f a probability density function?
(b) Suppose that a continuous random variable X has probability
density function f. Compute EX. (Hint: Draw a picture of the
pdf.)
(c) Compute P(X > 2).
(d) Suppose that Y ~ Uniform(0, 3). Which random variable has the
larger variance, X or Y? (Hint: Draw a picture of the two pdfs.)
(¢) Determine and graph the cumulative distribution function of X.

3-w4cvhxmj.pdf 3-5dsog2ia-ymryt3dm.png

Monica · Accepted Answer

Solution 
a) The sum of probability density function is equal to one, to find the value of c equate the integral to 1 
b) To find the Expected value of X we have to multiply the integral with x and find the value of E(X) using the formula
c)
d) The variance of the uniform distribution is given by,

Consider the function f : R® — R defined by 0 z3 where c is an undetermined constant. (a) For what value of ¢ is f a probability density function? (b) Suppose that a continuous random variable X...

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