6. Suppose we have the cdf of a continuous distribution with random variable X given by the function for x <0 F(x) = (x5 – 2r3 + 2x) for 0 2 What is the probability that X is between 1 and 2? 3 А. 10 19 В. 20 1 C. 20 D. 1 E. None of the above 7. For pdf f(x), which is nonzero on the interval [a, b], the corresponding cdf on the interval [a, b) is given by F(x) = | 5(t)dt A. True B. False 8. For type I error a and type II error B, a = 1 – B. Α. True B. False

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6.
Suppose we have the cdf of a continuous distribution with random variable
X given by the function
for x <0
F(x) =
(x³ – 2x3 + 2x) for 0 <x < 2
20
for x > 2
What is the probability that X is between 1 and 2?
3
A.
10
19
1
C.
20
D. 1
E. None of the above
20
7.
For pdf f(x), which is nonzero on the interval [a, b], the corresponding cdf on
the interval [a, b] is given by
F(æ) = | f(t)dt
A. True
B. False
8.
For type I error a and type II error 3, a =1- B.
A. True
B. False
B.
Transcribed Image Text:6. Suppose we have the cdf of a continuous distribution with random variable X given by the function for x <0 F(x) = (x³ – 2x3 + 2x) for 0 <x < 2 20 for x > 2 What is the probability that X is between 1 and 2? 3 A. 10 19 1 C. 20 D. 1 E. None of the above 20 7. For pdf f(x), which is nonzero on the interval [a, b], the corresponding cdf on the interval [a, b] is given by F(æ) = | f(t)dt A. True B. False 8. For type I error a and type II error 3, a =1- B. A. True B. False B.
Expert Solution
Step 1

Calculation Part:

6)

The cdf of X is given by

F(X)=0,                           for x<0

F(X)={1/20(x5-2x3+2x)}, for 0≤X≤2

F(X)=1,                           for x>1

To find Probability that X lies between 1 and 2:

P(1<X<2)=F(2)-F(1)

Note: P(a<X<b)=F(b)-F(a)

now we have to find F(2) and F(1) separately

F(2)=1/20(25-2*23+2*2)

F(2)=1/20(32-16+4)

F(2)=1/20(20)

F(2)=1

F(1)=1/20(15-2*13+2*1)

F(1)=1/20(1-2+2)

F(1)=1/20(1)

F(1)=1/20

substitute F(1) and F(2) in above to get P(1<X<2)

P(1<X<2)=F(2)-F(1)

P(1<X<2)=1-(1/20)

P(1<X<2)=19/20

Result:

The Probability that X lies between 1 and 2 is 19/20

Hence, the option b is correct.

 

 

 

 

 

 

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