.The number of major software failures of an update to the PearOS ranges from 0 to 5 and has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution. x 0 1 2 3 4 5 p(x)        .20     a     .21     .15     .11     .02   F(x)        .20     .51     b     .87    .98    1   a. If p is the probability mass function for x, then evaluate a.  b. If F is the cumulative distribution function of x, then what is the value of b?  c. What is the expected value of x?

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.The number of major software failures of an update to the PearOS ranges from 0 to 5 and has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution.

x 0 1 2 3 4 5
p(x)        .20     a     .21     .15     .11     .02  
F(x)        .20     .51     b     .87    .98    1  

a. If p is the probability mass function for x, then evaluate a. 
b. If F is the cumulative distribution function of x, then what is the value of b? 
c. What is the expected value of x? 
d. Calculate the variance of x. 
e. Calculate the expected value of 
x3 + 2x
 
f. The PearOS is updated 3 times. Assuming independence between updates, what is the probability the total number of errors on the 3 updates is 0. (i.e., no errors) 
g. The PearOS is updated 3 times. Assuming independence between updates, what is the probability the total number of errors on the 3 updates is 1. (i.e., 1 total error) 
h. The PearOS is updated 3 times. Assuming independence between updates, what is the probability the total number of errors on the 3 updates is no more than 1. 
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