Optional Topics

In the Optional Topic of "Discrete Mathematics," which of the following is a valid representation of a relation from set A = {1, 2} to set B = {a, b} that is a function?

In the Optional Topic of "Statistics and Probability," if X is a continuous random variable with probability density function f(x) = 2x for x in [0,1], what is the expected value E(X)?

In the Optional Topic "Discrete Mathematics," the number of onto functions from a set with 3 elements to a set with 2 elements is:

In the Optional Topic "Statistics and Probability," the variance of a binomial distribution with parameters n and p is:

In the Optional Topic "Discrete Mathematics," the number of ways to arrange the letters of the word 'INDIA' such that the vowels are always together is:

In the Optional Topic "Statistics and Probability," if two events A and B are independent and P(A) = 0.4, P(B) = 0.5, find P(A ∪ B).

In the Optional Topic "Discrete Mathematics," the number of subsets of a set with 5 elements having exactly 3 elements is:

In the Optional Topic "Statistics and Probability," a normal distribution has mean μ = 50 and standard deviation σ = 5. What is the probability that a value lies between 45 and 55? (Use empirical rule)

In the Optional Topic "Discrete Mathematics," how many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5 if repetition is allowed and the number is divisible by 5?

In the Optional Topic "Statistics and Probability," if the correlation coefficient between two variables X and Y is -0.8, which of the following is true?