Question

4. Suppose a random variable has the following probability mass functions: [ p(1)=frac{1}{2}, p(2)=frac{1}{4}, p(3)=frac{1}{8}, p(4)=frac{1}{8} ] (i) Find and sketch the cdf of the random variable ( X ). (ii) Find ( p(X leq 1), p(1<X<3) ) and ( p(1 leq X leq 3) ).

          4. Suppose a random variable has the following probability mass functions:
[
p(1)=frac{1}{2}, p(2)=frac{1}{4}, p(3)=frac{1}{8}, p(4)=frac{1}{8}
]
(i) Find and sketch the cdf of the random variable ( X ).
(ii) Find ( p(X leq 1), p(1<X<3) ) and ( p(1 leq X leq 3) ).

$4. Suppose a random variable has the following probability mass functions: [ p(1)=frac12, p(2)=frac14, p(3)=frac18, p(4)=frac18 ] (i) Find and sketch the cdf of the random variable ( X ). (ii) Find ( p(X leq 1), p(1<X<3) ) and ( p(1 leq X leq 3) ).$

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Applied Statistics and Probability for Engineers

Douglas C. Montgomery, George C. Runger 5th Edition

Chapter 3

Instant Answer

Solved by Expert Donna Densmore

05/22/2024

Step 1

For the given probability mass function, we can calculate the cdf as follows: For $ x < 1 $, $ F(x) = 0 $ because the random variable X cannot take values less than 1. For $ 1 \leq x < 2 $, $ F(x) = p(1) = \frac{1}{2} $. For $ 2 \leq x < 3 $, \( F(x) Show more…

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