The probability density function, f(x), for any continuous random variable X, represents:Group of answer choicesthe probability that X takes on a specific value x.the height of the function at x.                                      the area under the curve at x.all possible values that X will assume within some interval a £ x £ b.

What is the area under f(x) if the function is a continuous probability density function?

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?Multiple ChoiceThe area under f over all values that are x or less.The area under f over all values x.The area under f over all non-negative values that are x or less.The area under f over all values that are x or more.

Regarding continuous probability functions, the area under the graph represents the ________.

The proportion of a population that is contained within an interval corresponds to an area under the probability ▼(Choose one) curve.

Suppose X is a continuous random variable with the following probability density func-tion:f (x) = c(2 − x), 0 ≤ x ≤ 2(a) [2 marks] Plot the probability density function, clearly marking on your plot thevalues of f (x) when x = 0 and x = 2 and labelling both axes.(b) [2 marks] Explain and show why the value of c must equal 12 .(c) [2 marks] Find P (1 < X < 1.5).(d) [3 marks] Find P ({1 < X < 1.5}|{X > 0.5}).(e) [2 marks] Find P ({X > 0.5}|{1 < X < 1.5}).(f) [4 marks] Suppose that we have another random variable U that is uniformlydistributed with parameters 2 and 4. That is, the probability density function of Uis given byf (u) = 12, 2 ≤ u ≤ 4.Further, U and X are independent. In addition, someone has told us that therandom variable Y defined byY = X + Uhas expected value equal to 113 and variance equal to 59 . Based on this information,calculate the expected value and variance of X