Question

In: Math

For a poisson distribution where X ~ Pois(u), solve the questions below. Please show all work...

For a poisson distribution where X ~ Pois(u), solve the questions below. Please show all work and all steps.

a.) Show that the pmf is a pmf using the criteria for verifying pmf (2 conditions).

b.) Show that E(X) = u

c.) Show that Var(X) = u

Expert Solution

Let ,

Therefore , the probability mass function of X is ,

; x=0,1,2,..........

= 0 ; otherwise

a) Now, we shall verify that P(X) is a probability mass function

(i) ; for all x

(ii)

b)

; Since the term corresponding to x=0 is zero

; Since ,

c) The second raw moment is ,

; Since ,

; Since the term corresponding to x=0 and x=1 are zero

Therefore ,

$Var(X)=\mu_{2}^{'}-\mu_{1}^{'}^2=\mu^2 +\mu-\mu^2=\mu$

milcah answered 8 months ago

Please solve all of the questions, questions 1, 2, and 3. Please show all work and...

Please solve all of the questions, questions 1, 2, and 3. Please show all work and all steps. 1.) Find x(t) = Σ aktk such that tx'' = x 2.) Find x(t) = Σk>=0 aktk such that x'' = tx + 1 and x(0) = 0, x'(0) = 1 3.) Using the Frobenius method, solve t2x'' - 3tx' + (4-t)x = 0

Please solve questions 1 and 2. Please show all work and all steps. 1.) Find the...

Please solve questions 1 and 2. Please show all work and all steps. 1.) Find the solution xa of the Bessel equation t2x'' + tx' + t2x = 0 such that xa(0) = a 2.) Find the solution xa of the Bessel equation t2x'' + tx' + (t2-1)x = 0 such that x'a(0) = a

Please solve the following questions. Please show all work and all steps. 1a.) Find CDF of...

Please solve the following questions. Please show all work and all steps. 1a.) Find CDF of the Bernoulli Distribution. 1b.) Explain your reasoning for part 1a above. Do not use a series result. 2a.) For the geometric distribution, show that the geometric pdf is actually a pdf (all probabilities are greater than or equal to 0 and the sum of the pdf from x=1 to x=infinity is equal to 1). 2b.) Find E(X) for 2a above. 2c.) Find V(X) for...

Please solve the questions below and show your work. Thank you. The town of Utopia has...

Please solve the questions below and show your work. Thank you. The town of Utopia has three equal-size groups of people: (i) type A people consistently prefer larger public parks to smaller; type B people prefer small public parks to large public parks, and they prefer large size to medium size parks; type C people most prefer medium size to small size public parks, which they in turn prefer by a modest amount to large levels. a. Draw on a...

Please solve the below (step by step, show all work): Consider a 10-year note with a...

Please solve the below (step by step, show all work): Consider a 10-year note with a coupon rate of 5%. Calculate its price assuming: 5% yield-to-maturity, annual compounding 5% yield-to-maturity, semi-annual compounding 6% yield-to-maturity, annual compounding 6% yield-to-maturity, semi-annual compounding

Please solve all parts of the following question. Please show all work and all steps. 1a.)...

Please solve all parts of the following question. Please show all work and all steps. 1a.) Solve x' = x + 3y + 2t y' = x - y + t^2 1b.) Solve x' + ty = -1 y' + x' = 2 1c.) Solve x' + y = 3t y' - tx' = 0

Please answer the questions in the space provided below each question. Show all of your work...

Please answer the questions in the space provided below each question. Show all of your work and circle your final answer. You forecast there are three potential scenarios for the economy: a bull, flat, and bear market. You also estimate the returns for a stock and bond mutual fund as follows: Economic Scenario Stock Fund Bond Fund Probability of Scenario Recession -18% 6% 0.3 Flat 8% 4% 0.45 Boom 20% -8% 0.25 Using this information, you find for the stock...

Consider the function f(x) = cos (bx2), where b = 0.0628cm−2. PLEASE SHOW ALL WORK AND...

Consider the function f(x) = cos (bx2), where b = 0.0628cm−2. PLEASE SHOW ALL WORK AND EXPLAIN THOROUGHLY! Equation Q12.8: [λx]2=-4π2f(x)d2f/dx2 (a) Argue that this function has crests at x = 0, 10 cm, 14.1cm, 17.3 cm, 20 cm, 22.4 cm, and so on. (b) Draw a graph of this function and show that it is like a wave whose wavelength decreases as x increases. (c) Estimate this function’s local wavelength at x = 20cm by averaging the distances to...

Please answer the problem below for all parts. Please show all work and write clearly. Thanks....

Please answer the problem below for all parts. Please show all work and write clearly. Thanks. (Apply total probability and Bayes’ rules) A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 22% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 28% at the Lakeview Motor Lodge. If the plumbing is faulty in 5% of the rooms at the Ramada Inn,...

Please show all work and formula: Please use the information on the table below to answer...

Please show all work and formula: Please use the information on the table below to answer this question. Security Actual Return Beta A 12% 1.2 B 10% 1.0 C 14% 1.4 Assume the risk-free interest rate is 1% and the market risk premium is 5.5%. An investor would like to invest $40,000 in Security A, $25,000 in security B and $50,000 in Security C. Find the portfolio’s expected return. Find the portfolio’s actual return. Based on your answers to a...