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January 5, 2019

## Expected value (mean): The average of the all the possible outcomes of the random

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## General guidance

Concepts and reason

Expected value (mean): The average of the all the possible outcomes of the random variable is called as the expected value of the probability distribution. The outcomes for the random variable can be either the probability outcomes or the relative frequencies of the variable.

In Statistics, the long run average value obtained by repetitions for the given experiment is termed as expected value for the random variable X. Also, the random variable can be of discrete and continuous type. Moreover, as the number of repetitions is increased, the arithmetic mean of the values is approximately nearer to the expected value. The expected value of the random variable X is usually denoted by E(X).

Fundamentals

The formula for the expected value of the discrete random variable is,

E\left( X \right) = \sum {X\,P\left( X \right)}

Also, E\left( {X – a} \right) = E\left( X \right) – a

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FIRST STEP | ALL STEPS | ANSWER ONLY

## Step-by-step

### Step 1 of 5

(a.1)

The expected cash prize is obtained as shown below:

It is mentioned that, grand price is $14,000,000. Also, let X is a random variable denoting cash prize That is, \begin{array}{c}\\E\left( X \right) = \sum {X\,P\left( X \right)} \\\\ = 0.242573\\\end{array} Part a.1The expected cash prize is$0.24.

Explanation | Hint for next step

The expected cash prize is obtained by multiply each of the probabilities wi

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