Select all statements that are true for density curves.(a) the total area under the curve is 1.(b) the proportion of data values between two numbers a and b is the area under the curve between a and b .(c) the curve is symmetric and single-peaked.(d) the curve satisfies the 68-95-99.7% rule.(e) the curve is on or above the horizontal axis.

(A), (B), (E)

(A) The total area under the curve is 1.

True, by definition if we have a probability distribution we need to satisfy:

Assuming off course that

(B) The proportion of data values between two numbers a and b is the area under the curve between a and b .

True. If we assume continuous random variable the probability is given by:

(E) The curve is on or above the horizontal axis.

True. Is a conditions neccesary in order to satisfy a probability density function:

Because we can't have negative probabilities

Step-by-step explanation:

Let X a continuous random variable with probability density function

(A) The total area under the curve is 1.

True, by definition if we have a probability distribution we need to satisfy:

Assuming off course that

(B) The proportion of data values between two numbers a and b is the area under the curve between a and b .

True. If we assume continuous random variable the probability is given by:

(C) The curve is symmetric and single-peaked.

False. Counterexample: The Chi square distribution is not symmetric but satisfy the conditions for a density function. Other counter examples are the Gamma or the Beta distribution.

(D) The curve satisfies the 68-95-99.7% rule.

False. This rule only applies for a normal distribution and not for all the other possible denisty functions like : Gamma, Beta, Exponential, Dirichlet, etc.

(E) The curve is on or above the horizontal axis.

True. Is a conditions neccesary in order to satisfy a probability density function:

Because we can't have negative probabilities

(A), (B), (E)

answer: x=3 and y=4

step-by-step explanation: