Question

In: Math

Consider a hyper geometric probability distribution with n=7, R= 8 and N=17 a) calculate P(x =5)...

Consider a hyper geometric probability distribution with n=7, R= 8 and N=17

a) calculate P(x =5)

b) calculate P(x=4)

c) calculate P(x <=1)

d) calculate the mean and strandard deviation of this distribution

Expert Solution

Probability function of a Hyper geometric

Given, n=7, R= 8 and N=17

a) calculate P(x =5);

Substituting 5 in the below probability function

p(x=5) = 0.1037

b)

calculate P(x =4);

Substituting 4 in the below probability function

p(x=4) = 0.3023

c) calculate P(x <=1)

P(x<=1) = P(x=0) + P(x=1)

P(x<=1) = P(x=0) + P(x=1) = 0.00185+0.03455=0.03640

P(x <=1) = 0.03640

d) mean and standard deviation of this distribution

Standard deviation = 1.044

Mean = 3.2941

Standard deviation = 1.044

milcah answered 1 year ago

Discuss the difference between the Poisson and Hyper-geometric probability distribution. When would each of these be...

Discuss the difference between the Poisson and Hyper-geometric probability distribution. When would each of these be used? Describe a scenario for each.

Find the following probabilities. A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7. B.)...

Find the following probabilities. A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7. B.) P(X = 5), X following a Uniform distribution on the interval [3,7]. c.) P(X = 5), X following a Normal distribution, with µ = 3, and σ = .7. (To complete successfully this homework on Stochastic Models, you need to use one of the software tools: Excel, SPSS or Mathematica, to answer the following items, and print out your results directly from the software....

For a binomial probability distribution, n = 130 and p = 0.60. Let x be the...

For a binomial probability distribution, n = 130 and p = 0.60. Let x be the number of successes in 130 trials. a. Find the mean and standard deviation of this binomial distribution. a. Find the mean and the standard deviation of this binomial distribution. b. Find to 4 decimal places P(x ≤ 75) using the normal approximation. P(x ≤ 75) = c. Find to 4 decimal places P(67 ≤ x ≤ 72) using the normal approximation. P(67 ≤ x...

Consider the following. n = 8 measurements: 4, 3, 7, 8, 5, 6, 4, 6 Calculate...

Consider the following. n = 8 measurements: 4, 3, 7, 8, 5, 6, 4, 6 Calculate the sample variance, s2, using the definition formula. (Round your answer to four decimal places.) s2 = Calculate the sample variance, s2 using the computing formula. (Round your answer to four decimal places.) s2 = Find the sample standard deviation, s. (Round your answer to three decimal places.) s =

Consider a hypergeometric probability distribution with nequals4, Requals4, and Nequals10. a) Calculate P(xequals0). b) Calculate P(xgreater...

Consider a hypergeometric probability distribution with nequals4, Requals4, and Nequals10. a) Calculate P(xequals0). b) Calculate P(xgreater than1). c) Calculate P(xless than4). d) Calculate the mean and standard deviation of this distribution. a) P(xequals0)equals nothing (Round to four decimal places as needed.) b) P(xgreater than1)equals nothing (Round to four decimal places as needed.) c) P(xless than4)equals nothing (Round to four decimal places as needed.) d) The mean of this distribution is nothing. (Round to three decimal places as needed.) The standard...

Compute the mean and variance of the following probability distribution. x P(x) 5................................. .1..

Compute the mean and variance of the following probability distribution.x P(x)5................................. .110............................... .315............................... .220............................... .4

A 5th filter is described by the difference equation: 2y(n)=2 x(n)+7 x(n-1)+3 x(n-2)-8 x(n-3)+ x(n-4)-8 x(n-5)+7...

A 5th filter is described by the difference equation: 2y(n)=2 x(n)+7 x(n-1)+3 x(n-2)-8 x(n-3)+ x(n-4)-8 x(n-5)+7 y(n-1)-3 y(n-2)+5y(n-3)- y(n-4) Determine the frequency response. Plot the magnitude and the phase response of this filter. Consider the plot -π≤w≤π for 501 points. Describe the magnitude response (Low pass filter, High Pass filter, etc.) Determine the system stability. Determine the impulse response h(n). You may set the period to -100≤n≤100 Determine the unit step response for -100≤n≤100 . (Matlab)

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1,...

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1, 2, ..., and 0 < p < 1. This form of the geometric starts at x = 0, not at x = 1. Given are the following properties: E(X) = (1-p)/p, and Var(X) = (1-p)/p^2 A random sample of size n is drawn; the data are X1, X2, ..., Xn. A. Derive the Fisher information function for the parameter p. B. Find the Cramér-Rao...

Suppose X = 20, n = 50 a. Calculate the estimate for p, the true probability...

Suppose X = 20, n = 50 a. Calculate the estimate for p, the true probability of success b. Calculate and interpret a 90% Confidence interval for the true probability of success. c. You would like to know if p is actually greater than 1/3, so you test the following null hypothesis: H0: p ≤ 1/3 What is the alternative hypothesis? Conduct and interpret this test at the 0.05 significance level.

Suppose that X ~ NB(r, p) [negative binomial distribution] and that Y ~ B(n, p) [binomial]....

Suppose that X ~ NB(r, p) [negative binomial distribution] and that Y ~ B(n, p) [binomial]. a. Give a probabilistic argument to show that P(X > n) = P(Y < r). b. Use the FPF to express the equality in part (a) in terms of PMFs. c. Using the complementation rule, how many terms of the PMF of X must be evaluated to determine P(X > n)? d. How many terms of the PMF of Y must be evaluated to...