Solution Found!
Let X1,X2, . . . ,X36 be a random sample of size 36 from
Chapter 5, Problem 13E(choose chapter or problem)
Let \(X_{1}, X_{2}, \ldots, X_{36}\) be a random sample of size 36 from the geometric distribution
with pmf \(f(x)=(1 / 4)^{x-1}(3 / 4), x=1,2,3, \ldots\) Approximat
(a) \(P\left(46 \leq \sum_{i=1}^{36} X_{i} \leq 49\right)\)
(b) \(P(1.25 \leq \bar{X} \leq 1.50)\).
Hint: Observe that the distribution of the sum is of the discrete type.
Questions & Answers
QUESTION:
Let \(X_{1}, X_{2}, \ldots, X_{36}\) be a random sample of size 36 from the geometric distribution
with pmf \(f(x)=(1 / 4)^{x-1}(3 / 4), x=1,2,3, \ldots\) Approximat
(a) \(P\left(46 \leq \sum_{i=1}^{36} X_{i} \leq 49\right)\)
(b) \(P(1.25 \leq \bar{X} \leq 1.50)\).
Hint: Observe that the distribution of the sum is of the discrete type.
ANSWER:Step 1 of 4
Let X be a geometric random variable with parameter \(\text { 'p'}\).
The probability mass function for a geometric distribution is given by,
\(f(x)=(1-p)^{x-1} p, x=1,2,3, \ldots \ldots\)
The mean and variance are given by,
\(\begin{array}{l}
\mu=\frac{1}{p} \\
\sigma^{2}=\frac{1-p}{p^{2}}
\end{array}\)