200+ Probability-and-statistics Questions

Probability-and-statistics Questions Set 11:

Quiz Mode

If 'a' is a constant, then the expected value of 'a', E(a), is:

a^2

Solution:

What is the probability that a leap year will have 53 Mondays?

53/366

2/7

1/7

4/365

Solution:

If X and Y are Random Variables, then E(X - Y) is:

E(X) + E(Y)

E(Y) - E(X)

E(X) - E(Y)

-E(X).E(Y)

Solution:

If x is normally distributed with mean 12 and standard deviation = 4, what is the value of P(x ≤ 20)?

0.228

0.977

0.879

0.133

Solution:

Let's say there are two events A and B, such that P(A) = 0.8, P(B) = 0.6, and P(A|B) = 0.2. What is the value of P(A|~B)?

0.8

0.2

0.4

0.6

Solution:

If X and Y are random variables, and a and b are constants, then find the variance of Y if Y = aX + b.

a.V(X)

a.V(X) + b

(a+b).V(X)

a^2.V(X)

Solution:

A player tosses 3 coins. They win Rs 10 if 3 heads appear, Rs 5 if 2 heads appear, Rs 1 if 1 head appears, and lose Rs 12 if no heads appear. What is the expected amount the player will win?

Rs 2 gain

Rs 2 loss

Rs 5 gain

Rs 3.5 gain

Solution:

A point is randomly selected with uniform probability in the X-Y plane within the rectangular region with corners at (0,0), (1,0), (1,2) and (0,2). If P is the length of the position vector of the point, the expected value of P² is

5/3

2/3

4/3

Solution:

What are the expressions for the skewness and kurtosis of the Poisson distribution?

Skewness = 1/mean, Kurtosis = 3 + 1/(mean)

Skewness = mean, Kurtosis = 1/mean

Skewness = 3 + 1/(mean), Kurtosis = 1/mean

Skewness = 2/mean, Kurtosis = 6 + 2/(mean)

Solution:

An examination has 150 multiple-choice questions (MCQs) with 4 options each. Each correct answer is worth 1 mark, and for each wrong answer, there is a negative marking of -0.25 marks. If 1000 students choose their answers by random guessing, what is the sum of the total expected marks obtained by all these students?

2550

7525

9375

Probability-and-statistics Questions Set 11:

If 'a' is a constant, then the expected value of 'a', E(a), is:

Solution:

What is the probability that a leap year will have 53 Mondays?

Solution:

If X and Y are Random Variables, then E(X - Y) is:

Solution:

If x is normally distributed with mean 12 and standard deviation = 4, what is the value of P(x ≤ 20)?

Solution:

Let's say there are two events A and B, such that P(A) = 0.8, P(B) = 0.6, and P(A|B) = 0.2. What is the value of P(A|~B)?

Solution:

If X and Y are random variables, and a and b are constants, then find the variance of Y if Y = aX + b.

Solution:

A player tosses 3 coins. They win Rs 10 if 3 heads appear, Rs 5 if 2 heads appear, Rs 1 if 1 head appears, and lose Rs 12 if no heads appear. What is the expected amount the player will win?

Solution:

A point is randomly selected with uniform probability in the X-Y plane within the rectangular region with corners at (0,0), (1,0), (1,2) and (0,2). If P is the length of the position vector of the point, the expected value of P² is

Solution:

What are the expressions for the skewness and kurtosis of the Poisson distribution?

Solution:

Solution:

Related Question Sets:

Related Topics:

Probability-and-statistics Questions Set 11:

If 'a' is a constant, then the expected value of 'a', E(a), is:

Solution:

What is the probability that a leap year will have 53 Mondays?

Solution:

If X and Y are Random Variables, then E(X - Y) is:

Solution:

If x is normally distributed with mean 12 and standard deviation = 4, what is the value of P(x ≤ 20)?

Solution:

Let's say there are two events A and B, such that P(A) = 0.8, P(B) = 0.6, and P(A|B) = 0.2. What is the value of P(A|~B)?

Solution:

If X and Y are random variables, and a and b are constants, then find the variance of Y if Y = aX + b.

Solution:

A player tosses 3 coins. They win Rs 10 if 3 heads appear, Rs 5 if 2 heads appear, Rs 1 if 1 head appears, and lose Rs 12 if no heads appear. What is the expected amount the player will win?

Solution:

A point is randomly selected with uniform probability in the X-Y plane within the rectangular region with corners at (0,0), (1,0), (1,2) and (0,2). If P is the length of the position vector of the point, the expected value of P2 is

Solution:

What are the expressions for the skewness and kurtosis of the Poisson distribution?

Solution:

Solution:

Related Question Sets:

Related Topics:

A point is randomly selected with uniform probability in the X-Y plane within the rectangular region with corners at (0,0), (1,0), (1,2) and (0,2). If P is the length of the position vector of the point, the expected value of P² is