The width of a purple sea urchin varies uniformly from 4.75 cm to 10.5 cm. a)...
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The width of a purple sea urchin varies uniformly from 4.75 cm to 10.5 cm.
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a) Define the random variable of interest, X.
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b) State the distribution of X.
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c) Calculate the average width of a purple sea urchin.
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d) Suppose we knowP(5.2_<X_<7.1)=P(k_<X_<10.3). Find the value of k.
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e) Determine the probability that P(9 _< X _< 12)
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Homework Answers
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The width of a purple sea urchin varies uniformly from 4.75 cm
to 10.5 cm.
a)...
1.) Suppose that a box contains 8 cameras and that 3 of them are defective. A...
1.)
Suppose that a box contains 8 cameras and that 3 of them are
defective. A sample of 2 cameras is selected at random. Define the
random variable X as the number of defective cameras in the
sample.
Hint: Make a probability tree for selecting 2 cameras without
replacement.
Write the probability distribution for X.
k
P(X=k)
What is the expected value of X?
2.)
Assume that a procedure yields a binomial distribution with a
trial repeated n=5n=5 times. Find...
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
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X ~ N(60, 13). Suppose that you form random samples of 25 from this distribution. Let...
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1. X ~ N(50, 12). Suppose that you form random samples of 25 from this distribution....
1. X ~ N(50, 12). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(8 < X < 47) = 2.Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a...
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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. a. What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deviation? b. What is the distribution for the mean weight of 100 25-pound lifting weights? c. Find the probability that the mean actual...
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1.)
Suppose that a box contains 8 cameras and that 3 of them are
defective. A sample of 2 cameras is selected at random. Define the
random variable X as the number of defective cameras in the
sample.
Hint: Make a probability tree for selecting 2 cameras without
replacement.
Write the probability distribution for X.
k
P(X=k)
What is the expected value of X?
2.)
Assume that a procedure yields a binomial distribution with a
trial repeated n=5n=5 times. Find...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
Problem 1 A subway train on the #5 line arrives every eight minutes. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution In each appropriate box you are to enter either a rational number in "p/" format or a decimal value accurate to the nearest 0.01 a. The waiting time is modeled by a random variable X with X (pick on distribution b. The density function...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...
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