Probability, Random Variables, and Probability Distributions

Two random variables X and Y have means of 25 and 35 and standard deviations of 8 and 12, respectively. If Z = X + 2Y, what is the mean of Z?

What is the variance of the sum of two independent random variables X and Y if Var(X) = 4 and Var(Y) = 9?

How should one adjust for different types units when adding random variables X (measured in pounds) and Y (measured in kilograms)?

Which type of sampling method involves dividing the population into groups and then randomly selecting entire groups for inclusion in the sample?

Given two independent random variables $Z_1$ and $Z_2$ that both follow standard normal distributions, what is $P(Z_1 - Z_2 \\leq z)$ when $z=0$?

What is the probability that at least one out of two independent events will occur if Event A has a probability of occurring as $P(A)=0.40$ and Event B has $P(B)=0.30$?

If X and Y are independent random variables with known distributions, what is the probability distribution of the sum (X + Y) if X has a mean of 5 and standard deviation of 2, and Y has a mean of 3 and standard deviation of 4?

If the average time it takes two students A and B to complete a puzzle separately is 30 minutes each with a standard deviation of 5 minutes and also independent of the other, what is the standard error for the time it takes them completing the puzzle together?

If X and Y are independent random variables with means of 30 and 50 respectively, what is the expected value (mean) of their sum (X+Y)?

How does the probability distribution of a sum of two identical dice change compared to a single die roll?