Probability

Suppose that for a random sample of size 10, the value of covariance between two variables X and Y is 100 and the standard deviations of X and Y are 5 and 20 respectively. What is the value of regression coefficient in regression of Y on X?

Given below are two statements :
Statement-I: Let (x₁, x₂) be the chosen bundle when prices are (p₁, p₂) and let (y₁, y₂) is some other bundle such that p₁x₁+p₂x₂ ≥ p₁y₁+ p₂y₂. Then if the consumer is choosing the most preferred bundle she can afford, we must have (x₁, x₂)>(x₁,x₂).
Statement-II: If one bundle is chosen when another could have been chosen, we can say that the first bundle is revealed preferred to the second.
In the light of the above statements, choose the correct answer from the options given below:

If you draw a random sample of size 25 from a population whose standard deviation is 10, what will be the standard error of sample mean?

Suppose that in a given college, proportion of admitted students who complete their degree is 0.7, what is the expected number of students who will complete their degree from a random sample of 20 students from a given batch?

For a random variable X, it is given that E(X²)=16 and E(X) = 2. What is the value of variance for this distribution?

Suppose the distribution of weights of students in a college is normal with mean 60 kg and standard deviation 3 kg. Which of the following areas from the standard normal distribution gives the probability of a randomly selected student having weight less than 66 kg?

Suppose that the manager of a store estimates the probability of any customer entering the store making a purchase is 0.3. What is the expected number of customers making a purchase from a randomly selected set of 10 customers?