Find E[X], and Var[X], when "X" is a normal random variable with pa- rameter µ and o? respectively.
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- Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175A researcher administers a treatment to a sample of n=36 selected from a population with u=30 and o=2. If the sample mean after treatment is M=32, then Cohen’s d=1.00. True or False?Let m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.
- 4. The standard deviation of X, denoted SD(X), is given by SD(X) = Var(X). Find SD(aX + b) if X has variance of o?.Find the first two moments about the mean for the random variable X defined by X = -2 with prob. 1/3 3 with prob. 1/2 = 1 with prob. 1/6. %3DSuppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.
- If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? ExplainYou are performing a right-tailed test.If α=.01α=.01, find the critical value, to three decimal places.zα =A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…
- Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.ndependent random samples are selected from two populations and are used to test the hypothesis Hn: (H, - H2) = 0 against the alternative H,: (4, - H2) #0. An analysis of 232 observations from population 1 and 311 from population 2 yielded p-value of 0.113. Complete parts a and b below. a. Interpret the results of the computer analysis. Use as0.10. A. Since this p-value exceeds the given value of a, there is insufficient evidence to indicate that the population means are different. O B. Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. OC. Since the given a value exceeds this p-value, there sufficient evidence to indicate that the population means are different. O D. Since this p-value exceeds the given value of , there is sufficient evidence to indicate that the population means are different. b. If the alternative hypothesis had been Ha: (H1 - H2) <0, how would the p-value change? Interpret the p-value…6. Find the median of an exponential random variable X with parameter 1 = 4. (The median of X is m iff P(X < m) = 0.5.) Does it differ from E(X)? Try to explain.