数理统计与应用代写 数理统计代写

Mathematical Statistics with Applications

MA4114 HW1

数理统计与应用代写 (1)Let the random variable X equal to the number of days that it takes a high risk driver to have an accident. Assume that X has an

(1)

Let the random variable X equal to the number of days that it takes a high risk driver to have an accident. Assume that X has an exponential distribution. If P(X < 50) = 0.25, compute

(a) P(X > 100|X > 50).

(b) E(X).

 

(2)

Cars arrive at a tollbooth at a mean rate of 3 cars every 10 minutes according to a Possion process. Find the probability that the toll collector will have to wait longer than 20 minutes before collecting the 5th toll.

 

(3)  数理统计与应用代写

A candy maker produces mints that have a label weight of 20.8 grams. Assume the distribution of the weight of these mints is N(21.37, 0.16).

(a) Suppose that 15 mints are randomly selected and weighted. Let Y  be the number of meints that weigh less than 20.8 grams. Find P(Y ≤ 2).

(b) Suppose that 3 mints are indepencently picked, what is the probability that their combined weight is more than 65 grams?

(c) Suppose that 2 mints are indepencently picked, what is the probability that their weights diffffer by less than 1 gram?

(d) Suppose that 30 mints are indepencently picked, what is the probability that their average weight is more than 21 grams?

 

 

(4)  数理统计与应用代写

Let f(x, y) = 2e^-x-y , 0 ≤ x ≤ y < ∞, be the joint pdf of X and Y . Find f_X(x) and f_Y (y), the marginal pdfs of X and Y , respectively. Are X and Y independent?

 

(5)

The pdf of X is f(x) = θx^θ-1 , 0 < x < 1, θ > 0. Let Y = −2θ ln(X). How is Y distributed?

 

(6)  数理统计与应用代写

Let X₁ , X₂ , and X₃ be mutually independent random variables with Poisson distributions with means 2, 1, and 4, respectively.

(a) Use the moment generating function technique to fifind the distribution of Y = X₁ + X₂ + X₃ .

(b) Compute P(3 ≤ Y ≤ 9).

 

(7)  数理统计与应用代写

Let X and Y equal the outcomes when two fair 6-sided dice are rolled. Let W = X + Y . Assuming independence, fifind the pmf of W when

(a) The fifirst die has 3 faces numbered 0 and three faces numbered 2, and the second die has its faces numbered 0, 1, 4, 5, 8, and 9.

(b) The faces on the fifirst die are numbered 0, 1, 2, 3, 4, and 5, and the faces on the second die are numbered 0, 6, 12, 18, 24, and 30.

 

 

 

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