Chapter 2 Section 3 Question 11
Question
Let $Y$ ~ $Binomial(10,\theta)$. Compute $P(Y = 10)$.
Answer
Author: Mohammad-Ali Bandzar| Date:Oct 16 2020
From Example 2.3.3 in the book we know: $$p\scriptsize{Y}\normalsize{(y)=P(Y=y)={n\choose y}\theta ^y(1-\theta)^{n-y}}$$ In this equation n represents the number of trials, $\theta$ represents the probability of a success and y represents the desired number of successful outcomes

we shall now plug in $n=10$, $y=10$ $$P(Y=y)={n\choose y}\theta ^y(1-\theta)^{n-y}$$ $$P(Y=10)={10\choose 10}\theta ^{10}(1-\theta)^{10-10}$$ $$P(Y=10)=\theta ^{10}(1-\theta)^{0}$$ $$P(Y=10)=\theta ^{10}$$