Please round your answer to 3 decimal points.A continuous random variable X has the following PDF:(X -0 < x < 2f(x)=otherwise(a) Find the value of k to make f(x) a legitimate probability density function.(b) What is the probability that X is smaller than 1.3?(c) Find the mean of X.(d) Find the variance of X.(e) What is the probability that X is within 0.3 of its mean?

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Please round your answer to 3 decimal points. A continuous random variable X has the following PDF: 0

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Question

Please round your answer to 3 decimal points.
A continuous random variable X has the following PDF:
(X -
0 < x < 2
f(x)
=
otherwise
(a) Find the value of k to make f(x) a legitimate probability density function.
(b) What is the probability that X is smaller than 1.3?
(c) Find the mean of X.
(d) Find the variance of X.
(e) What is the probability that X is within 0.3 of its mean?

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