A pizza store owner noticed that a random count (Y) of pizzas ordered by students who reside on campus has distribution shown below
Y 1 Probability 0.15
Y 2 Prob 0.40
Y 3 Prob 0.25
Y 4 Prob 0.20
1. Find expected number of pizza order E[Y]
2. Determine variance of Y
3. Assume the revenue (R) after selling Y pizzas is measured as
R=8 * Y - 10. Evaluate expected revenue after order is completed, that is E[R]
4. For the same variable R=8 * Y - 10, determine its variance
Var [R]
I am very confused on how to start this off can anyone help me
Of course! I can help you with those questions. Let's break them down step by step.
1. To find the expected number of pizza orders, E[Y], you need to multiply each possible value of Y by its corresponding probability, and then sum them up.
E[Y] = (1 * 0.15) + (2 * 0.40) + (3 * 0.25) + (4 * 0.20)
2. To determine the variance of Y, you need to calculate the average squared deviation from the expected value.
Var[Y] = (1 - E[Y])^2 * 0.15 + (2 - E[Y])^2 * 0.40 + (3 - E[Y])^2 * 0.25 + (4 - E[Y])^2 * 0.20
3. The revenue (R) after selling Y pizzas is measured as R = 8 * Y - 10. To evaluate the expected revenue, E[R], we can substitute the expected value of Y into the equation and calculate it.
E[R] = 8 * E[Y] - 10
4. For the same variable R = 8 * Y - 10, to determine its variance Var[R], we need to substitute the variance of Y into the equation and calculate it.
Var[R] = 8^2 * Var[Y]
Now that you have the formulas for each question, you can calculate the expected number of pizza orders, variance of Y, expected revenue, and variance of revenue. It's important to note that "E" denotes the expected value and "Var" denotes the variance.