Answer the following question accordingly. It shouldn’t take that long. Thanks in advance! 1. Let Z be a Bernoulli random variable, Z ~ Bernoulli(0.7)Find the value of E[Z^23041]Round to the nearest hundredth if necessary

Answered: 1. Let Z be a Bernoulli random…

1. Let Z be a Bernoulli random variable, Z ~ Bernoulli(0.7 Find the value of E[Z^23041] Round to the nearest hundredth if necessary

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Answer the following question accordingly. It shouldn’t take that long. Thanks in advance!

1. Let Z be a Bernoulli random variable, Z ~ Bernoulli(0.7)
Find the value of E[Z^23041]
Round to the nearest hundredth if necessary

Expert Solution

Step 1

A random variable X is said to follow the Bernoulli distribution if its takes only non-negative values and its probability mass function is given by:

$P (X = x) = p^{x} . q^{(1 - x)}; x = 0, 1 . . . (1)$

Here, $q = 1 - p$ . It is denoted by $X ~ Bernoulli (p)$ . The mean of the Bernoulli distribution is p and its variance is p(1-p). The r^th moment is calculated as follows:

$E (X^{r}) = \sum_{i} {(x_{i})}^{r} . p (x)$

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