Easy 10 question probablility/ststs multiple choice problems

Question 1 of 10

10.0 Points

Which of the following is true is X is a continuous random variable, and f(x) is the probability density function of X?

A.f(x) ≥ 0
B.All of the given statements are true
C.The area under the entire graph of f(x) equals to 1.
D. For any two numbers a and b with a ≤ b, P (a≤ X ≤ b) = ∫ab f(x)dx

Question 2 of 10

10.0 Points

Which of the following statements is an example of a continuous random variable?

A.All of the given variables are continuous
B.The depth of Lake Michigan at a randomly chosen point on the surface
C.The number of credit hours you have this semester
D.The number of gas stations in Detroit

Question 3 of 10

10.0 Points

The cumulative distribution function F(x) for a continuous random variable X is defined for every number x by which of the following inequalities?

A.F(x) = 1 - P(X ≤ x)
B.F(x) = P(X ≤ x)
C.F(x) = P(X ≥ x) - P(X ≤ x)
D.F(x) = P(X ≥ x)
Question 4 of 10

Let X be a continuous random variable with probability density function f(x) and cumulative distribution function F(x). Then for any two numbers a and b with a < b, which of the following is true?

A.P (a≤ X ≤ b) = F(a) – F(b)
B.F(x) = (x – a)/(a - b)
C.P(X > a) = 1 - F(a)
D.P(X > b) = F(b) – 1

5) Which of the following is true about the median  м  of a continuous distribution?

A. м  is the 75th percentile
B. The area under the density curve to the right of  м  is larger than the area to the left of м.
C. м  satisfies F( м ) = 1
D. м  is the 50th percentile

6) If the probability density function of a continuous random variable X is f(x) = kx2 if 0 ≤ x ≤ 2 and f(x) = 0, if x > 2 or x < 0, then the value of parameter k is

A.0.25
B.any positive value greater than 2
C.0.375
D.2.0

7) A continuous random variable X is uniformly distributed on the interval [A,B], then the probability density function between A and B has a value of

A.(A-B)
B.(B-A)
C.(A+BX)
D.(A+B)/2
E.1/(B - A)

8) A continuous random variable X is uniformly distributed on the interval [35, 45]. The probability that X is between 40 and 50 is

A.0.6
B.0.7
C.0.1
D.0.5

9) Which of the following statements is NOT true if the probability density function of a continuous random variable X is f(x) = 5e-5x; x ≥ 0?

A.All of the given statements are not true.
B.E(X) = 0.20
C.P(X < 1) = 0.993
D.Var(X) = 0.02
E. The cumulative distribution function of X is F(x) = 1 - e-5x ; x ≥ 0

10) According to Chebyshev’s Theorem, what is the probability that random variable X is within 2.5 standard deviations from its expected value?

A.at least 75%
B.at least 89%
C.at least 84%
D.95%
E.82%