1. Suppose X and Y are a bivariate continuous random variable with 0sXs2 and 0SYS3 and have a valid joint PDF: f(x.y) = c (x2 + y12). Rounded to TWO decimal places the value of c is and the conditional probability Prí1
1. Suppose X and Y are a bivariate continuous random variable with 0sXs2 and 0SYS3 and have a valid joint PDF: f(x.y) = c (x2 + y12). Rounded to TWO decimal places the value of c is and the conditional probability Prí1
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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![10. Suppose X and Y are a continuous bivariate random variable with 0sXs 1 and 0 SYS2 and valid joint PDF f(x,y) = c (1+x/2+y/4).
Rounded to THREE decimal places, the value of c is
and the value of E[XY] is
11. Suppose X and Y are a bivariate continuous random variable with 0s Xs2 and 0sY s 3 and have a valid joint PDF:
f(x.y) = c (x2 + y/2).
Rounded to TWO decimal places the value of c is
and the conditional probability Pr[1<Y<2| X=0.5] is
12. The claim that a coin is fair is to be tested. Let p denote the probability that "head" is observed when the coin is tossed. The null hypothesis is, therefore, Ho : p=0.5. The test is carried out by
tossing the coin 6 times and counting the number of "heads" observed. Let X denote the number of "heads" so that X is B(6, p). It is suspected that the coin is weighted towards "heads".
Researcher A proposes a Rejection rule: A) Reject Ho if |X-3| = 3.
Researcher B proposes a Rejection rule: B) Reject Ho if X2 5.
Rounded to TWo decimal places the Probability of a Type I error for Rejection Rule A is
Suppose that the alternative is H : p = 0.7.
Rounded to Two decimal places the Probability of a Type Il error for Rule A is
*Note: make sure you perform any sub-calculations to sufficient accuracy so that your final answer is corect to the required decimal places.
and for Rejection Rule B it is
and for Rejection Rule B it is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F694fce0b-4aa0-4f40-88ae-a3e75435a12b%2F8e1548a9-99b3-4135-93d8-2c3804c8170d%2Fit4k81_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. Suppose X and Y are a continuous bivariate random variable with 0sXs 1 and 0 SYS2 and valid joint PDF f(x,y) = c (1+x/2+y/4).
Rounded to THREE decimal places, the value of c is
and the value of E[XY] is
11. Suppose X and Y are a bivariate continuous random variable with 0s Xs2 and 0sY s 3 and have a valid joint PDF:
f(x.y) = c (x2 + y/2).
Rounded to TWO decimal places the value of c is
and the conditional probability Pr[1<Y<2| X=0.5] is
12. The claim that a coin is fair is to be tested. Let p denote the probability that "head" is observed when the coin is tossed. The null hypothesis is, therefore, Ho : p=0.5. The test is carried out by
tossing the coin 6 times and counting the number of "heads" observed. Let X denote the number of "heads" so that X is B(6, p). It is suspected that the coin is weighted towards "heads".
Researcher A proposes a Rejection rule: A) Reject Ho if |X-3| = 3.
Researcher B proposes a Rejection rule: B) Reject Ho if X2 5.
Rounded to TWo decimal places the Probability of a Type I error for Rejection Rule A is
Suppose that the alternative is H : p = 0.7.
Rounded to Two decimal places the Probability of a Type Il error for Rule A is
*Note: make sure you perform any sub-calculations to sufficient accuracy so that your final answer is corect to the required decimal places.
and for Rejection Rule B it is
and for Rejection Rule B it is
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