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What is the probability that a standard normal variable takes on a value between -2.3 and 0.14?
What is the probability that a standard normal variable takes on a value between -2.3 and 0.14?
- 0.7449
- 0.6449
- 0.5449 (correct)
- 0.4449
What is the memoryless property of exponential distribution?
What is the memoryless property of exponential distribution?
- P (Y > s + t|Y > t) = P (Y > s + t); s, t ≥ 0
- P (Y > s + t|Y > t) = P (Y > t); s, t ≥ 0
- P (Y > s|Y > t) = P (Y > s); s, t ≥ 0
- P (Y > s + t|Y > t) = P (Y > s); s, t ≥ 0 (correct)
What is the approximate probability that a normal random variable Y takes on a value less than or equal to -7, given a moment-generating function m(t) = e^(-5t+6t^2)?
What is the approximate probability that a normal random variable Y takes on a value less than or equal to -7, given a moment-generating function m(t) = e^(-5t+6t^2)?
- 0.282 (correct)
- 0.211
- 0.233
- 0.104
What is the marginal density for Y2, given the joint density p(y1, y2)?
What is the marginal density for Y2, given the joint density p(y1, y2)?
What is the value of F(3, -1), given the joint probability density f(y1, y2) = 4, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1?
What is the value of F(3, -1), given the joint probability density f(y1, y2) = 4, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1?
What is the marginal density for Y1, given the joint probability density f(y1, y2) = 4, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1?
What is the marginal density for Y1, given the joint probability density f(y1, y2) = 4, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1?
What is the expression for the marginal density of Y1?
What is the expression for the marginal density of Y1?
What is the value of Cov(Y1, Y2) given that E(Y1 Y2) = 3/40?
What is the value of Cov(Y1, Y2) given that E(Y1 Y2) = 3/40?
What is the conditional density of Y1 given Y2?
What is the conditional density of Y1 given Y2?
What is the condition for Y1 and Y2 to be independent?
What is the condition for Y1 and Y2 to be independent?
What is the moment generating function of a random variable X?
What is the moment generating function of a random variable X?
What is the value of E(Y1Y2) for the given joint density f(y1,y2) = 6(1-y2) for 0 <= y1 <= y2 <= 1?
What is the value of E(Y1Y2) for the given joint density f(y1,y2) = 6(1-y2) for 0 <= y1 <= y2 <= 1?
What is the moment generating function of a Bernoulli random variable X with probability p?
What is the moment generating function of a Bernoulli random variable X with probability p?
What is the moment generating function of a binomial random variable X with parameters n and p?
What is the moment generating function of a binomial random variable X with parameters n and p?
What is the expression for the marginal density of Y2?
What is the expression for the marginal density of Y2?
What is the value of the conditional density f(y1|y2) at y1 = 0.5 and y2 = 0.7?
What is the value of the conditional density f(y1|y2) at y1 = 0.5 and y2 = 0.7?
What is the moment generating function of a Poisson random variable X with parameter λ?
What is the moment generating function of a Poisson random variable X with parameter λ?
What is the moment generating function of a normal random variable X with mean µ and variance σ²?
What is the moment generating function of a normal random variable X with mean µ and variance σ²?
What is the conditional mean of Y given X = x in a linear function form?
What is the conditional mean of Y given X = x in a linear function form?
If X and Y are independent random variables, what is the value of Cov(X, Y)?
If X and Y are independent random variables, what is the value of Cov(X, Y)?
What is the formula for the variance of the sum of X and Y?
What is the formula for the variance of the sum of X and Y?
What is the value of P(x + y ≤ 1) given the joint probability density function f(x, y) = 4(1-xy) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1?
What is the value of P(x + y ≤ 1) given the joint probability density function f(x, y) = 4(1-xy) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1?
What is the correlation coefficient, ρxy, for the joint probability density function f(x, y) = 4(1-xy) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1?
What is the correlation coefficient, ρxy, for the joint probability density function f(x, y) = 4(1-xy) for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1?
What is the conditional mean of Y given X = x, in terms of the mean and standard deviation of Y, and the correlation coefficient ρxy?
What is the conditional mean of Y given X = x, in terms of the mean and standard deviation of Y, and the correlation coefficient ρxy?
What is the moment generating function (MGF) of an exponential random variable X with parameter λ?
What is the moment generating function (MGF) of an exponential random variable X with parameter λ?
What is the joint probability distribution involving two random variables called?
What is the joint probability distribution involving two random variables called?
If X and Y are independent random variables, what is the relationship between their joint probability distribution and their individual probability distributions?
If X and Y are independent random variables, what is the relationship between their joint probability distribution and their individual probability distributions?
What is the notation for the conditional probability distribution of Y given X = x?
What is the notation for the conditional probability distribution of Y given X = x?
What is the covariance of X and Y in terms of their means and expectations?
What is the covariance of X and Y in terms of their means and expectations?
What is the range of the correlation coefficient, ρxy?
What is the range of the correlation coefficient, ρxy?
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