Answered: Consider the probablility model with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A population of values is normally distributed with μ = 84.5 and σ = 85.3. a) Find P72 for a single randomly selected value. This answer represents the score separating the bottom 72% scores from the top 28% scores. P72 = b) Now draw a random sample of size n = 96. Find P72 for the sampling distribution. This answer represents the score separating the bottom 72% of the sample means from the top 28% of the sample means. P72 = Enter your answers as numbers accurate to 1 decimal place.
Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y)=-6 E(Z) =7 Var (X) = 31 Var(Y) = 34 Var(Z)=5 E(X)=2 Compute the values of the expressions below. E(5-5Y)= 0 (")-0 %3D Var(3Y+5) = 0 E(-x') - 0
MP3 player comes in 3 configurations : $80, $100, and $120. Let X denote the cost of a single randomly selected MP3 player purchase with probability distribution given by X 80 100 120 p(x) 0.2 0.3 0.5 with u = E(X) = 106, ♂² Conduct a SRS of size 2. ✪ Calculate a statistic X. ● Find the sampling distribution for X. = V(X) = 224
Let X₁, X₂, ..., Xn be a random sample of size n from a geometric distribution for which p is the probabil- ity of success. (a) Use the method of moments to find a point estimate for p. (b) Explain intuitively why your estimate makes good sense.
2b)
A population consists of 1, 1, 1, 2, 2, 3 and 4 (i) List all possible samples of size n= 3 without replacement. (ii) Obtain the sampling distribution of X. (iii) Verify that: uz =u and N - n N - 1
state whether or not this resulting observed interval ended up capturing the true population proportion p of 0.45.
A fair coin is tossed three times. Let X be number of heads. (1) Write out the sample space. (2) Find P(X=2) (3) Find E(X)
rom the set of numbers {4,6, 8}, a random sample of size 2 is selected with replacement. (a) Determine the sampling distribution of the sample mean X. (b) Find the mean E(X) of the sampling distribution of the sample mean X. Compare E(X) with the population mean u.
Let X1, X2......,X100 be independent binomial random variables with parameter p=0.25. The sample mean is : (First image) a. Find the value of E(X) and Var(X). b. State the sampling distribution of X and explain why has the sampling distribution stated. c. Find P(X<25.5). d. Find (second image)
For a binary response y, let ỹ be the proportion of ones in the sample (which is equal to the (i) sample average of the y,). Let ĝo be the percent correctly predicted for the outcome y = 0 and let 9, be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly predicted, show that p is a weighted average of ĝo and q1: p = (1 – y)ao + 5ª1- (ii) In a sample of 300, suppose that ỹ = .70, so that there are 210 outcomes with y, = 1 and 90 with y; = 0. Suppose that the percent correctly predicted when y = 0 is 80, and the percent correctly predicted when y = 1 is 40. Find the overall percent correctly predicted.

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Consider the probablility model with sample space {A,B,C} and P(A)=0.5, P(B)=0.4, P(C)=0.1.Then (a) P( A or C ) = . (b) P( B and C ) =