Question

Suppose that Y is a binomial random variable based on n trials with success probability p and consider Y? = n ? Y. a Argue that for y? = 0, 1, . . . , n P (Y? = y?) = P (n ? Y = y?) = P (Y = n ? y?). b Use the result from part (a) to show that P (Y? = y?) = ?(n ? y? over n) p^n?y? q^y? = ?(n over y?) q^y? p^n?y?.

          Suppose that Y is a binomial random variable based on n trials with success probability p and
consider Y? = n ? Y.
a Argue that for y? = 0, 1, . . . , n
P (Y? = y?) = P (n ? Y = y?) = P (Y = n ? y?).
b Use the result from part (a) to show that
P (Y? = y?) = ?(n ? y? over n) p^n?y? q^y? = ?(n over y?) q^y? p^n?y?.

Suppose that Y is a binomial random variable based on n trials with success probability p and
consider Y? = n ? Y.
a Argue that for y? = 0, 1, . . . , n
P (Y? = y?) = P (n ? Y = y?) = P (Y = n ? y?).
b Use the result from part (a) to show that
P (Y? = y?) = ?(n ? y? over n) p^n?y? q^y? = ?(n over y?) q^y? p^n?y?.

Added by Denise B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

10/18/2022

Step 1

Therefore, Y* = n - Y also follows a binomial distribution with parameters n and 1-p. Show more…

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Suppose that Y is a binomial random variable based on n trials with success probability p, and consider Y* = n - Y. Argue that for y = 0,..n, P(Y* = y) = P(n - Y = y) = P(Y = n - y). Use the result from part (a) to show that P(Y* = r) = (