Discrete random variable

Which is NOT a discrete random variable?

• Number of heads obtained when a coin is being thrown 3 times.

• Height of students in a class.

• Number of '6's obtained when 4 dice are thrown.

• Score of students in a common test.

Answer explanation

If the outcomes of your variables are not continuous, e.g. integers, it is a discrete random variable.

The following is the probability distribution table of X.

What is the probability of P(X<3)?

• 1/8

• 1/2

• 7/8

• 1

If X~B(10,p), how do we calculate P(X > 2)?

• Binomcdf(10,p,2)

• 1-binompdf(10,p,2)

• 1-binomcdf(10,p,2)

• 1-binomcdf(10,p,1)

Answer explanation

P(X>2) = 1 - (PX<=2), so you need to use 1- binomial cumulative probability 2.

What are the traits of a binomial distribution? Tick all which are applicable.

• There are unlimited number of trials that is conducted.

• There is a limited number of trials.

• Probability of success is constant.

• There are only 2 possible outcomes

Which of the following scenarios belong to a binomial distribution? Click those that are correct.

• Number of heads obtained when a coin is being thrown 3 times.

• Height of students in a class.

• Number of '6's obtained when 4 dice are thrown.

• Score of students in a common test.

Answer explanation

Only the first is correct. You need to check the 3 traits: (1) 2 outcomes - success / failure (2) constant probability of success (3) n independent trials.

The number of '6's does not meet (1) & (2). Heights are continuous random variable. Scores does not meet the conditions too.

Which of the following statements best describe the expected value of a discrete random variable?

• It is the average of all possible outcomes.

• It is the weighted average of all possible outcomes.

• It is the geometric average of all possible outcomes

• It is the complex average of all possible outcomes in the distribution.

How would you interpret a very small variance or standard deviation but not equal to 0?

• The values of the random variables are farther from the mean.

• The values of the random variables are nearer to the mean.

• The values of the random variables are equal to the mean.

• The values of the random variables have no relationship with the mean.

If X and Y are independent random variable, how do you calculate E(3X-4Y)?

• 3E(X)+4E(Y)

• 3E(X)-4E(Y)

• 9E(X)+16E(Y)

• 9E(X)-16E(Y)

If X and Y are independent random variable, how do you calculate Var(3X-4Y)?

• 3Var(X)-4Var(Y)

• 3Var(X)+4Var(Y)

• 9Var(X)-16Var(Y)

• 9Var(X)+16Var(Y)

If Wi is independent random variable from a distribution W, what is the Var(W1+W2+W3)?

• 3 Var (W)

• 9 Var (W)