Exercise 4.32. The nth factorial moment of a random variable Y is defined as the expectation E[Y(Y −1)···(Y −n+1)]. (a) Suppose that Y ∼ Poisson(μ). Find an exact expression for the nth factorial moment of Y . Hint. Use a similar argument as the one used in the proof of Fact 4.18. (b) Compute the third moment E(Y 3) of Y ∼ Poisson(μ).

good luck!

cutie~

y=1/4x-4

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: