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STA4321 HW3(2)

# STA4321 HW3(2) - STA 4321 Introduction to Probability...

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STA 4321 I ntroduction to P robability T heory Assignment 3 Assigned Friday February 12 Due Monday February 22 Show your work to receive full credit. 1. A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. A sample of 5 nurses is to be selected from a total of 20 nurses employed in the hospital. Eight of the 20 nurses are male. Let X represent the number of male nurses in the sample of 5 nurses. (a) Find the probability mass function (p.m.f) of X and plot it. (b) Find the cumulative distribution function (c.d.f) of X and plot it. (c) Find E ( X ) and V ( X ). 2. (a) Verify that the function f ( x ) deﬁned by f ( x ) = p (1 - p ) x - 1 x =1,2,. . . and f ( x ) = 0 otherwise, is a p.m.f of a discrete random variable. (b) Suppose Steve Nash’s career free throw percentage ( FT %) is 90%. Suppose we tell him to shoot FT 0 s indeﬁnately. Let X represent the number of FT’s until he misses for the ﬁrst time. Assuming that FT 0 s attempts are independent, what is

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STA4321 HW3(2) - STA 4321 Introduction to Probability...

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