Derive a formula for the cdf

Assignment Help Basic Statistics

Reference no: EM131824738

Let X and Y be continuous random variables. Define a new random variable Z according to the following process. First flip a biased coin with probability α of obtaining a head. If the result is heads, sample from X; otherwise sample from Y . Such a distribution is called a mixture of X and Y.

a) Derive a formula for the cdf of Z in terms of α and the cdfs of X and Y.

b) Derive a formula for the pdf of Z in terms of α and the pdfs of X and Y . c) Let W ∼ 0.3 · Norm(8, 2) : 0.7 · Norm(16, 3) (that is, a 30-70 mix of two normal distributions). What is P(W ≤ 12)?

Reference no: EM131824738

Questions Cloud

Prepare a monthly operating budget for dmv for fiscal year : Prepare a monthly operating budget for the DMV for the fiscal year ending August 31, 2014. Determine the operating surplus and deficit for each month.

Studying the relationship between honesty : Cheaters. study components. Researchers studying the relationship between honesty, age and self-control conducted an experiment on 160 children

What should simon report : Simon owns 50% of the stock of Cargill Corporation, a calendar year taxpayer that has elected Subchapter S status. What should Simon report for 2010

What must be true about prices in the two industries : Entrepreneurs shift capital and labor across industries in pursuit of profit. Let's look at this a little more closely. Suppose there are two industries.

Derive a formula for the cdf : a) Derive a formula for the cdf of Z in terms of a and the cdfs of X and Y.

What is the most practical and easily applied lesson learned : Review and reflect on what you learned. What is the most practical and easily applied lesson you learned? What was the hardest to grasp? Why?

Define rate of return on capital investments : Suppose that two industries, the pizza industry and the calzone industry, are equally risky, but rates of return on capital investments are only 5% in the pizza

What is a transfer price : What is a transfer price? What role does GAAP play in how firms determine transfer prices

Develop a likelihood ratio test to test : Develop a likelihood ratio test to test H0 : µ = µ0 vs. Ha : µ = µ0 when our model is X iid ~ Norm(µ, 1).

User Account

All Pages