t X be a random variable with a variance of 5. Find the varian und to 4 decimal places if needed.
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- Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator ofA freight company is shipping boxes that have an expected value of 2000 TL. The variance of the value of boxes is 40,000 TL². The expectation of the number of boxes that are damaged as a result of falling as they are being moved is 60. The variance in the number of boxes that are damaged (due to these falls) is 90. The number of damaged boxes and the value of each box is independent. Let S represent the total value of damage incurred as a result of all of the boxes that fell. a) Calculate E[S]. b) Calculate Var[S].If a random variable X ∼ Exponential(1). Find the distribution of Y = X/λ.
- Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately ?2 = 47.1. However, a random sample of 18 colleges and universities in Kansas showed that x has a sample variance s2 = 86.1. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance. ased on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient…A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1).Find its mean value and variation.2. Let X - tp. Verify the mean and variance formulas. (Hint: Let X = p/2UV-1/2.)
- Find the approximate mean and variance of Y = √X, where X is a randomvariable following a Poisson distribution.If X~Gamma(4,6) the the variance of X is 4 24 144 LOThe maximum patent life for a drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below, where Y is a random variable representing actual patent life of a drug (in years): y P(Y=y) F(y) 4 5 6 7 8 9 10 11 0.06 0.08 0.11 0.15 0.22 0.18 0.12 0.08 a) Complete the table above with the cumulative probability distribution for actual patent life (F(y) = P(Y ≤ y)). b) What is the probability that the actual patent life of a random drug is 6 years or less? c) What is the probability that the actual patent life of a random drug is more than 8 years? Show this in two ways: i. using the probability distribution for Y ii. using the cumulative probability distribution for Y, and applying our probability of comple-…