Question

​a) Define your random​ variables, and use them to express the​ farmer's net income. A. Apounds of apples​ sold, ​, B. Aprice per pound of​ apples, ​, C. Apounds of apples​ sold, ​, D. Aprice per pound of​ apples, ​, ​b) Find the mean. The mean profit is 62 dollars. ​c) Find the standard deviation of the net income. The standard deviation is nothing dollars. ​(Round to two decimal places as​ needed.) ​d) Do you need to make any assumptions in calculating the​ mean? A. ​Yes; the prices must be independent. B. ​Yes; the variables must be discrete. C. ​Yes; the prices must be dependent. D. ​No; no assumptions are made in calculating the mean. Do you need to make any assumptions in calculating the standard​ deviation? A. ​Yes; the prices must be independent. B. ​Yes; the prices must be dependent. C. ​Yes; the variables must be discrete. D. ​No; no assumptions are made in calculating the standard deviation. Click to select your answer(s).

Answer 1

Please find the complete question in the attached file:

Explanation:

For point a:

When X was its random variable of apples, Y the randomized variables of potatoes, then

`\to 100\ X + 50\ Y - 2`

Your gross profit is represented.

For point b:

The expected value varies as per the random variables:

`\to \mu=100 \mu_(X)+50 \mu_(Y)-2=100(0.5)+50(0.3)-2=\$ 63`

For point c:

Its variance varies to the square of coefficient (without constants) as well as the standard variance is dependent upon on square root:

`\sigma=\sqrt{100^2\sigma_(X)^2 +50^2 \sigma_(Y)^2}\=√(10,000(0.2^2) + 2500(0.1^2)) \approx \$20.62`

For point d:

Yes, because prices are dependent on the apple as well as the prices of potatoes.