Suppose you are offered a commission-based job that pays you 20% of your daily expected sales revenue. On any given day, there is an 80% chance you make $100 in sales and a 20% chance you make $1,000 in sales. What is your expected income for that day?数值题

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Let ( 𝐴 1 , 𝐴 2 , 𝐴 3 , 𝐴 4 ) be events with 𝑃 ( 𝐴 𝑖 ) = 0.3 . For each ( 𝑖 ). Define 𝑌 = 𝐼 𝐴 1 + 𝐼 𝐴 2 + 𝐼 𝐴 3 + 𝐼 𝐴 4 .   No independence assumptions are given. Which statement must be true?

A machine flips 4 coins. The probability that the [math: i]th coin lands heads is [math: pi], where:[math: p1=0.5] [math: p2=0.7] [math: p3=0.8] [math: p4=0.9] What is the expected value of the total number of heads observed?[Fill in the blank]

Microhard Inc.’s management is considering the following three scenarios of their firm stock value in the future. If the economy is booming, the Microhard Inc. share price will increase by 85%; in a bad scenario, the stock price will go down by 35%; and if everything stays as it is, the stock price will increase by 15%. The chances of observing any of the scenarios are equal. What is the expected return of Microhard Inc. shares?[Fill in the blank]

Peter does a lot of commuting by cycle.  Occasionally he gets a puncture while out riding (and very occasionally two).  Peter wants to determine the expected value for the number of punctures on a ride, so that he can determine how many puncture repair patches he should purchase to get him through 100 rides. Let x be the number of punctures on a given ride. The probability of getting one puncture is p(1) = 0.08 The probability of getting two punctures is p(2) = 0.01 The probability of getting zero punctures is 1 - p(1)-p(2) Find the expected value for the number of punctures for a given ride and multiply this by 100 and then round to the nearest integer to determine how many patches Peter should purchase.  Type your answer below.

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