Probability Distributions and Characteristics

What is a key characteristic of a continuous random variable in a normal distribution?

• It is always equal to zero.

• It can take any value along the x-axis.

• It can only take integer values.

• It is restricted to positive values.

How is the probability of a continuous random variable determined?

• By counting the number of possible outcomes.

• By measuring the area under the curve.

• By finding the highest point on the curve.

• By calculating the sum of all values.

What is the probability that a continuous random variable equals a specific value?

• It depends on the value.

• It is always 0.

• It is always 1.

• It is equal to the mean.

In a uniform distribution, what is the probability density function f(x) when the range is from A to B?

• A + B

• B - A

• 1 / (B + A)

• 1 / (B - A)

What is the mean of a uniform distribution ranging from A to B?

• (A + B) / 2

• 2 * (A + B)

• A - B

• B / A

What is the standard deviation formula for a uniform distribution?

• (B - A) / 2

• (B + A) / 2

• (B - A) / sqrt(12)

• sqrt(B - A)

What is the y-intercept in an exponential distribution?

• The mean

• Lambda, the rate parameter

• The standard deviation

• The median

How do you calculate the probability that X is less than a given value in an exponential distribution?

• lambda * X

• 1 / (lambda * X)

• e^(lambda * X)

• 1 - e^(-lambda * X)

What is the formula for the probability that X is greater than a given value in an exponential distribution?

• lambda / X

• X / lambda

• e^(-lambda * X)

• 1 - e^(lambda * X)

What is the total area under the curve for any continuous probability distribution?

• It is always 0.

• It is equal to the mean.

• It varies depending on the distribution.

• It is always 1.