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Expected Value and Variance

Description: This quiz covers the concepts of expected value and variance in probability.
Number of Questions: 14
Created by:
Tags: expected value variance probability
Attempted 0/14 Correct 0 Score 0

What is the expected value of a random variable $X$?

  1. The average value of $X$

  2. The sum of all possible values of $X$

  3. The probability of $X$ taking on a particular value

  4. The standard deviation of $X$


Correct Option: A
Explanation:

The expected value of a random variable $X$ is the average value of $X$ over all possible outcomes.

What is the variance of a random variable $X$?

  1. The average value of $X$

  2. The sum of all possible values of $X$

  3. The probability of $X$ taking on a particular value

  4. The standard deviation of $X$ squared


Correct Option: D
Explanation:

The variance of a random variable $X$ is the expected value of the squared deviation of $X$ from its mean.

If the expected value of a random variable $X$ is 5 and its variance is 4, what is the standard deviation of $X$?

  1. 2

  2. 4

  3. 6

  4. 8


Correct Option: A
Explanation:

The standard deviation of $X$ is the square root of the variance of $X$, which is 4. Therefore, the standard deviation of $X$ is 2.

If the expected value of a random variable $X$ is 0 and its variance is 1, what is the probability that $X$ takes on a value between -1 and 1?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: A
Explanation:

The probability that $X$ takes on a value between -1 and 1 is given by the area under the normal distribution curve between -1 and 1. This area is approximately 0.6827.

If the expected value of a random variable $X$ is 10 and its variance is 4, what is the probability that $X$ takes on a value greater than 12?

  1. 0.1587

  2. 0.3173

  3. 0.4772

  4. 0.6331


Correct Option: A
Explanation:

The probability that $X$ takes on a value greater than 12 is given by the area under the normal distribution curve to the right of 12. This area is approximately 0.1587.

If the expected value of a random variable $X$ is 5 and its variance is 9, what is the probability that $X$ takes on a value between 2 and 8?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: B
Explanation:

The probability that $X$ takes on a value between 2 and 8 is given by the area under the normal distribution curve between 2 and 8. This area is approximately 0.9545.

If the expected value of a random variable $X$ is 0 and its variance is 1, what is the probability that $X$ takes on a value less than -2?

  1. 0.0228

  2. 0.0455

  3. 0.0668

  4. 0.0893


Correct Option: A
Explanation:

The probability that $X$ takes on a value less than -2 is given by the area under the normal distribution curve to the left of -2. This area is approximately 0.0228.

If the expected value of a random variable $X$ is 10 and its variance is 4, what is the probability that $X$ takes on a value between 8 and 12?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: A
Explanation:

The probability that $X$ takes on a value between 8 and 12 is given by the area under the normal distribution curve between 8 and 12. This area is approximately 0.6827.

If the expected value of a random variable $X$ is 5 and its variance is 9, what is the probability that $X$ takes on a value greater than 10?

  1. 0.1587

  2. 0.3173

  3. 0.4772

  4. 0.6331


Correct Option: B
Explanation:

The probability that $X$ takes on a value greater than 10 is given by the area under the normal distribution curve to the right of 10. This area is approximately 0.3173.

If the expected value of a random variable $X$ is 0 and its variance is 1, what is the probability that $X$ takes on a value between -3 and 3?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: C
Explanation:

The probability that $X$ takes on a value between -3 and 3 is given by the area under the normal distribution curve between -3 and 3. This area is approximately 0.9973.

If the expected value of a random variable $X$ is 10 and its variance is 4, what is the probability that $X$ takes on a value less than 8?

  1. 0.1587

  2. 0.3173

  3. 0.4772

  4. 0.6331


Correct Option: A
Explanation:

The probability that $X$ takes on a value less than 8 is given by the area under the normal distribution curve to the left of 8. This area is approximately 0.1587.

If the expected value of a random variable $X$ is 5 and its variance is 9, what is the probability that $X$ takes on a value between 0 and 10?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: B
Explanation:

The probability that $X$ takes on a value between 0 and 10 is given by the area under the normal distribution curve between 0 and 10. This area is approximately 0.9545.

If the expected value of a random variable $X$ is 0 and its variance is 1, what is the probability that $X$ takes on a value greater than 2?

  1. 0.0228

  2. 0.0455

  3. 0.0668

  4. 0.0893


Correct Option: B
Explanation:

The probability that $X$ takes on a value greater than 2 is given by the area under the normal distribution curve to the right of 2. This area is approximately 0.0455.

If the expected value of a random variable $X$ is 10 and its variance is 4, what is the probability that $X$ takes on a value between 6 and 14?

  1. 0.6827

  2. 0.9545

  3. 0.9973

  4. 0.7357


Correct Option: B
Explanation:

The probability that $X$ takes on a value between 6 and 14 is given by the area under the normal distribution curve between 6 and 14. This area is approximately 0.9545.

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