Only need Parts D and E **Title: Understanding Probability and Decision Making with Pizza Choices**You don’t like pizza but all your friends love getting pizza so you always go with them and try a new topping and base sauce combination each time until you find a pizza that you like. The probability of you liking a pizza is 0.08. The average pizza costs $10 but your friends tell you that if you find a pizza that you like they will give you $80.---**Problem (a):**Let $ Y $ be the number of times you try a new pizza before you find one you like. What kind of distribution does $ Y $ follow? What would be its expected value and variance? Don’t round your answers.**Solution:**- Distribution: $ Y $ follows a geometric distribution since we are counting the number of trials until the first success (finding a pizza you like).- Expected Value: $ E(Y) = \frac{1}{p} = \frac{1}{0.08} = 12.5 $- Variance: $ \text{Var}(Y) = \frac{1-p}{p^2} = \frac{0.92}{(0.08)^2} = 143.75 $---**Problem (b):**You are determined to keep getting pizza until you find one that you like. When you finally find a pizza and your friends give you a congratulatory $80, will you have any profit? What will be the variance of this profit?**Solution:**- Cost to find a pizza you like: $ 10 \times E(Y) = 10 \times 12.5 = 125 $- Profit: $ 80 - 125 = -45 $ (a loss of $45)- Variance of cost: $ 10^2 \times \text{Var}(Y) = 100 \times 143.75 = 14375 $- As the profit is given by the reward minus the cost, the variance of the profit remains the same, i.e., 14375, assuming a fixed reward.---**Problem (c):**You only start off with $60. What is the probability that you lose all of your money before you manage to find a pizza that you enjoy? Round your answer to 3 decimal places.**Solution:**The scenario describes running out of money before a success. Since each trial (d) Assume that you won a competition and now have a lifetime supply of pizzas for yourself for free. You go out for pizza 38 times in a year. Let $ X $ be the number of times you like your pizza out of the 38 different pizzas that you try.What is the distribution of $ X $?(e) 1) Out of the 38 pizzas that you try, how many would you expect to like?2) What is the variance of the number of pizzas that you like? Round to 3 decimal places.

Let p be the probability of you liking the pizza. Given that p = 0.08

Answered: What is the distribution of X? 1) Out…

What is the distribution of X? 1) Out of the 38 pizzas that you try, how many would you expect to like? 2) What is the variance of the number of pizzas that you like? Round to 3 d

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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