Question

A book has n typos. The proofreader, Prune, catches each typo with probability $p$ and miss it with probability $1 - p$. Let X be the number of typos caught by Prune. (a) Write down the probability mass function of X. (b) Compute $E[(1+X)^2]$ (c) Compute the conditional probability $P(X ge 2|X ge 1)$ (d) Conditioned on $X = 1$, what is the probability that the 3rd typo is caught?

          A book has n typos. The proofreader, Prune, catches each typo with probability $p$ and miss it with probability $1 - p$. Let X be the number of typos caught by Prune.
(a) Write down the probability mass function of X.
(b) Compute $E[(1+X)^2]$
(c) Compute the conditional probability $P(X ge 2|X ge 1)$
(d) Conditioned on $X = 1$, what is the probability that the 3rd typo is caught?

A book has n typos. The proofreader, Prune, catches each typo with probability p and miss it with probability 1 - p. Let X be the number of typos caught by Prune.
(a) Write down the probability mass function of X.
(b) Compute E[(1+X)^2]
(c) Compute the conditional probability P(X ge 2|X ge 1)
(d) Conditioned on X = 1, what is the probability that the 3rd typo is caught?

Added by Ana D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ekaveera Kumar

03/27/2022

Step 1

Step 1: The probability mass function of X is given by the binomial distribution formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where $ k $ takes values from 0 to n. Show more…

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A book has n typos. The proofreader, Prune, catches each typo with probability p and miss it with probability 1 - p . Let X be the number of typos caught by Prune. (a) Write down the probability mass function of X. (b) Compute E[(1 + X)^2] (c) Compute the conditional probability P(X >= 2|X >= 1) (d) Conditioned on X = 1 , what is the probability that the 3rd typo is caught?