Question

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let $X$= the number of cars sold and $Y$= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of $X$and $Y$are as follows:

Define $D=X-Y$.

Compute $\sigma D$assuming that $X$and$Y$ are independent. Show your work

Short answer

From the given information, the standard deviation is$1.14$

Step-by-step solution

Given Information

It is given in the question that,

$\mu \chi =1.1,\sigma \chi =0.943$

$\mu \gamma =0.7,\sigma \gamma =0.64$

$D=\chi -\gamma$

Step 2: Explanation

The standard deviation can be calculated as:

$$\begin{gathered} {\sigma }_D=\sqrt{{\sigma }_X^2+{\sigma }_Y^2} \\ =\sqrt{{0.943}^2+{0.64}^2} \\ =\sqrt{1.2998} \\ =1.14 \end{gathered}$$