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Questions and Answers
What is the formula to calculate the expected value of a discrete random variable?
What is the formula to calculate the expected value of a discrete random variable?
- ∑xP(x) (correct)
- ∑x^2 - P(x)
- ∑x^2P(x)
- ∑P(x)/x
If X is a discrete random variable and Y = X^2, what is E(Y)?
If X is a discrete random variable and Y = X^2, what is E(Y)?
- E(X^3)
- E(X)^4
- E(X^2) (correct)
- E(X)^2
What is the variance of a binomial distribution with n trials and probability of success p?
What is the variance of a binomial distribution with n trials and probability of success p?
- np
- n/p
- n(1-p)
- np(1-p) (correct)
What is the probability of getting exactly 2 successes in 10 trials, where the probability of success is 0.5?
What is the probability of getting exactly 2 successes in 10 trials, where the probability of success is 0.5?
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What is the meaning of P(X ≤ 3) in a Poisson distribution?
What is the meaning of P(X ≤ 3) in a Poisson distribution?
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What is the formula to calculate the variance of a discrete random variable?
What is the formula to calculate the variance of a discrete random variable?
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Study Notes
Discrete Probability Distribution
- A discrete probability distribution table is given with values of x (0, 1, 2, 3, 4) and their corresponding probabilities (1/5, 1/5, 1/5, 1/5, 1/5)
- The expected value and variance of the discrete random variable need to be determined
Fair Die
- A normal 6-sided fair die is thrown 24 times and the number of 6's scored is recorded
- The mean and variance of the experiment need to be calculated
Random Variable X
- Random variable X takes values -1, 0, 1 with probabilities 1/8, 2/8, 5/8 respectively
- Need to compute E(X) and Var(X)
- Y = X^2, need to compute pmf of Y and E(Y)
Discrete Random Variable X
- X has a probability mass function (PMF) with values x = 1, 2, 3, 4 and probability cx, and x = 5 with probability 1/2
- Need to find the value of constant c, E(3X + 2) and Var(3X + 2)
Poisson Distribution
- X ~ Po(0.2), need to determine the following probabilities:
- P(X ≤ 3)
- P(X = 6)
- P(X > 0)
Binomial Distribution
- X ~ B(n = 10, p = 0.5), need to determine the following probabilities:
- P(X ≤ 2)
- E(X) and Var(X)
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