Each morning John eats some eggs. On any given morning, the number of eggs he eats is equally likelyto 1, 2, 3, 4, or 5 independent of what he has done in the past. Let X be the number of eggs that John eats in 10 days. Find the mean and the variance of X

Mean = 3

Variance = 2

Step-by-step explanation:

Since number of eggs he eats is equally likely to any 5 numbers, probability of each one will be (1/5) = 0.2

The probability mass function will therefore be

x 1 2 3 4 5

p 0.2 0.2 0.2 0.2 0.2

The mean is given as the expected value

And expected value is given as

E(X) = Σ xᵢpᵢ

where x = each possible sample space

p = probability of the sample space occurring.

E(X) = (1×0.2) + (2×0.2) + (3×0.2) + (4×0.2) + (5×0.2) = 3 eggs.

b) Variance is given by

Variance = Var(X) = Σx²p − μ²

where μ = E(X)

Σx²p = (1² × 0.2) + (2² × 0.2) + (3² × 0.2) + (4² × 0.2) + (5² × 0.2) = 0.2 + 0.8 + 1.8 + 3.2 + 5 = 11

Var(X) = Σx²p − μ² = 11 - 3² = 11 - 9 = 2

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

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step-by-step explanation: