statistics question

Question

A sales agent has received a job offer from a trading house that distributes electric stoves.

Suppose that X is the random variable that represents the number of kitchens sold in a week and that the probability distribution of those sales is.

x1 f(xi)

0 0.30

1 0.35

2 0.25

3 0.10

If the commercial house offers to pay the sales agent a flat rate of C$500 per week, plus C$300 for each kitchen sold, determine.

a) The sales agent's expected weekly income after many weeks.

b) The standard deviation of the agent's weekly income. Interpret the result.

Answer 1

a. For the expectation, by definition, you can take the summation of all x_i * f(x_i). So, the summation of 0*0.30 + ... + 3*0.10 will give you the expectation E[X].

b. For the standard deviation, it may be easier to calculate the variance, then take the square root. You can use the variance formula, Var(X) = E[X^2] - (E[X])^2. To find E[X^2], you can take the summation of all (x_i)^2 * f(x_i). Once you have the variance, take the square root to find the standard deviation. As for interpretation, think about the purpose of reporting a standard deviation or a variance. These values summarize the variability within a distribution.