Question : Find the value of k that makes f(x) = kx^3 a probability density function on the interval : 2163574

Determine whether the function is a probability density function over the given interval.

18) f(x) = (1/2), 4 ≤ x ≤ 10

A) Yes

B) No

19) f(x) = 5x, 0 ≤ x ≤ 1

A) No

B) Yes

20) f(x) = (1/2)x, 0 ≤ x ≤ 2

A) No

B) Yes

21) f(x) = (1/4)x, 4 ≤ x ≤ 7

A) No

B) Yes

22) f(x) = (3/31)x², 1 ≤ x ≤ 4

A) No

B) Yes

23) f(x) = (1/9)x², 0 ≤ x ≤ 3

A) Yes

B) No

24) Which of the graphs below could not possibly be the graph of a probability function f(x)?

A) graph B only

B) graphs B and C

C) graphs A and B

D) graphs A and C

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

25) Is f(x) = (1/21)x² a probability density function on the interval 1 ≤ x ≤ 4 ?

Enter "yes" or "no".

26) Is f(x) = (1/(x + 1)²) is a probability density function for x ≥ 0? If so, find P(X ≥ 2).

Enter either "no" or just a reduced fraction of form (a/b).

27) Is f(x) = ((3/2))x - 1 a probability density function for 0 ≤ x ≤ 2?

Enter "yes" or "no"

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find k such that the function is a probability density function over the given interval. Then write the probability density function.

28) f(x) = k; -2 ≤ x ≤ 4

A) 6; f(x) = 6

B) (1/6); f(x) = (1/6)

C) -2; f(x) = -2

D) - (1/2); f(x) = - (1/2)

29) f(x) = k(14 - x); 0 ≤ x ≤ 14

A) 14; f(x) = 14(14 - x)

B) (1/98); f(x) = (1/98)(14 - x)

C) (1/196); f(x) = (1/196)(14 - x)

D) 196; f(x) = 196(14 - x)

30) f(x) = (k/x); 1 ≤ x ≤ 17

A) ln17; f(x) = xln17

B) (2/ln17); f(x) = (2/xln17)

C) (1/ln17); f(x) = (1/xln17)

D) 1 - ln17; f(x) = (x/1 - ln17)

31) Find the value of k that makes f(x) = kx a probability function on the interval 1 ≤ x ≤ 2.

A) (4/5)

B) (2/3)

C) (2/5)

D) (6/5)

E) none of these

32) A random variable X has probability density function f(x) = ke^-kx (x ≥ 1) for some constant k. Suppose that Pr(1 ≤ X ≤ 2) = (1/4), what is the value of k?

A) (1/4)

B) ln2

C) (3/2)ln2

D) (1/2)ln2

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

33) Find the value of k that makes f(x) = kx³ a probability density function on the interval 0 ≤ x ≤ 1.

Enter just an integer.

34) Find the value of k that makes f(x) = k√(x) a probability density function on the interval 4 ≤ x ≤ 9.

Enter just a reduced fraction.