Let x be the damage incurred(in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities .8, .1, .08, and .02, respectively. A particular company offers a 500$ deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?
Let X be exponentially distributed with parameter λ > 0. Find the PMF of Y = ⌈X⌉, where, given a real number x, ⌈x⌉ denotes the rounding of x to the nearest integer whose value is greater or equal to x. Identify the distribution of Y .
(b) State the null and alternate hypotheses. choose one
1. (H0: μ < 4.8; H1: μ = 4.8) 2. (H0: μ > 4.8; H1: μ = 4.8) 3. (H0: μ = 4.8; H1: μ ≠ 4.8) 4. (H0: μ = 4.8; H1: μ > 4.8)
5. (H0: μ = 4.8; H1: μ < 4.8)
(c)What is the value of the sample test statistic? (Round your answer to three decimal places.)
(d)Find the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? choose one
1. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. 2. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. 3. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 4. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant (f) Interpret your conclusion in the context of the application. choose one1. There is sufficient evidence at the 0.01 level to conclude that the population mean RBC count for the patient is lower than 4.80. 2. There is insufficient evidence at the 0.01 level to conclude that the population mean RBC count for the patient is lower than 4.80.
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population.) A random sample of six Denver neighborhoods gave the following information:x 29 2 11 17 7 6y 173 35 132 127 69 53Σx=72, Σy=589, Σx^2=1340, Σy^2=72,277,Σxy=9499a) draw a scatter diagram for the datab) find x bar, y bar, b and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).c) Find the sample correlation coefficient r and the coefficient of determination. What percentage of the variation in y is explained by the least-squares model?d) Test the claim that the population correlation coefficient p is not zero at the 1% level of significance.e) For a neighborhood with x= 12% change in population in the past few years, predict the change in the crime rate (per 1000 residents)f) verify that Se= 22.5908g) Find a 80% confidence interval for the change in crime rate when the percentage change in population is x= 12% h) Test the claim that the slope B of the population least-squares line is not zero at the 1% level of significance.I) Find an 80% confidence interval for B and interpret its meaningshow all work!
Let X be a non empty set and d be the discrete metric on X. Let {xn } be a Cauchy sequence in (X,d).
xn = xk
Let X be a non-central (5, ) random variable, and Y, independent of X, be a (4) random variable.
a) Derive the moment generating function of 2X-1, and find its mean and variance.
b) Find the mean of W =
(a) P(Z ≥ 0.98)
(b) P(−1.1 ≤ Z ≤ 1.37)
(c) P(0.7 ≤ Z ≤ 1.7)
(d) P(−1.4 ≤ Z)
Let Z
be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c
such that
=P≤−c≤Zc0.9534.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Please answer the following question related to G-test, likelihood ratio test
Let Y1, Y2, Y5), be independent random variables with probability distributions that areNormal(m, (:2 = 1). That is, 1 — % (1;;- —Hi, )2B f(yé|#é)=m i=11253 _OO<,U"E<+OO The null hypothesisis of homogeneity states that all 3 random variables have the same Normaldistribution, i.e., Ho : p1 = pig = M3 = a. The alternative hypothesis states that at least 2 ofthe m’s are different. (a) Please derive G2, — for testing the null hypothesis of homogeneityversus the alternative hypothesis. Simplify as much as possible. (RECALL: 221:1 K; = n?) (b) What is the large sample probability distribution for G2 in this problem?
Let Y1 < Y2 < Y3 denote the order statistics of a random sample of size
3 from a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Let Z =
(Y1 + Y3)/2 be the midrange of the sample. Find the pdf of Z
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