dataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are in fact equal

Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).

A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs.   Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3   78.5     The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2            Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic =  p-value =  The p-value is     The correct…

The mean and variance of a binomial variate X are 4 and 4/3 respectively. Find P(X ≥ 3)