Urn 1 contains two white balls and one black ball. Urn 2 contains one white ball
ID: 3222508 • Letter: U
Question
Urn 1 contains two white balls and one black ball. Urn 2 contains one white ball and five black balls. First, one ball is drawn at random from urn 1 and placed in urn 2. A ball is then drawn at random from urn 2. The ball drawn out of urn 2 is white. Given this information, what is the probability that the ball pick from urn 1 and transferred to urn 2 was white?
Let X be the damage incurred (in dollars) in a certain type of accident during a given year. Possible values for X are 0, 1000, 5000, 10000 with probabilities 0.8, 0.1, 0.08, and 0.02 respectively. A particular company offers a 500 dollar deductible insurance policy. If the company wishes its expected profit to be 100 dollars, what premium amount should it charge?
A quiz consists of two parts. For a randomly selected student, let X = the number of points earned on the first part, and Y = the number of points earned on the second part. Below is the joint pmf for X and Y
p(x,y)
y
0
5
10
0
0.06
0.09
0.05
x
5
0.07
0.19
0.23
10
0.02
0.15
0.14
The final score for the test is defined as the maximum of X and Y. Compute the expected value of the final score.
A quiz consists of two parts. For a randomly selected student, let X = the number of points earned on the first part, and Y = the number of points earned on the second part. Below is the joint pmf for X and Y
p(x,y)
y
0
5
10
0
0.06
0.09
0.05
x
5
0.07
0.19
0.23
10
0.02
0.15
0.14
Compute the correlation between X and Y (Corr(X,Y))?
Urn 1 contains two white balls and one black ball. Urn 2 contains one white ball and five black balls. First, one ball is drawn at random from urn 1 and placed in urn 2. A ball is then drawn at random from urn 2. The ball drawn out of urn 2 is white. Given this information, what is the probability that the ball pick from urn 1 and transferred to urn 2 was white?
Let X be the damage incurred (in dollars) in a certain type of accident during a given year. Possible values for X are 0, 1000, 5000, 10000 with probabilities 0.8, 0.1, 0.08, and 0.02 respectively. A particular company offers a 500 dollar deductible insurance policy. If the company wishes its expected profit to be 100 dollars, what premium amount should it charge?
A quiz consists of two parts. For a randomly selected student, let X = the number of points earned on the first part, and Y = the number of points earned on the second part. Below is the joint pmf for X and Y
p(x,y)
y
0
5
10
0
0.06
0.09
0.05
x
5
0.07
0.19
0.23
10
0.02
0.15
0.14
The final score for the test is defined as the maximum of X and Y. Compute the expected value of the final score.
A quiz consists of two parts. For a randomly selected student, let X = the number of points earned on the first part, and Y = the number of points earned on the second part. Below is the joint pmf for X and Y
p(x,y)
y
0
5
10
0
0.06
0.09
0.05
x
5
0.07
0.19
0.23
10
0.02
0.15
0.14
Compute the correlation between X and Y (Corr(X,Y))?
Explanation / Answer
Q.1 Urn 1 contains two white balls and one black ball. Urn 2 contains one white ball and five black balls. First, one ball is drawn at random from urn 1 and placed in urn 2. A ball is then drawn at random from urn 2. The ball drawn out of urn 2 is white. Given this information, what is the probability that the ball pick from urn 1 and transferred to urn 2 was white?
Answer 1 : Urn 1 contains 2 white balls and 1 black ball
and Urn 2 contain 1 white and 5 black ball.
when we drawn a ball from urn 2 , it comes white
so it will be white
(i) when ball drawn from urn 1 is white [P(1W) = 2/3] and then urn 2 will have 2 white and 5 balck balls so P(2W) = 2/7
(ii) when ball drawn from urn 1 is black [p(1B) = 1/3] and then urn 2 will have 1 white and 6 black balls so P(2W) = 1/7
now we have to calculate the probabillity that the ball drawn from urn 1 was white
so P( 1W / 2W) = 2/3 * 2/7 / ( 2/3 + 2/7 + 1/3 * 1/7) = 4/21 / ( 4/21 + 1/21) = 4/5
Q>2 Let X be the damage incurred (in dollars) in a certain type of accident during a given year. Possible values for X are 0, 1000, 5000, 10000 with probabilities 0.8, 0.1, 0.08, and 0.02 respectively. A particular company offers a 500 dollar deductible insurance policy. If the company wishes its expected profit to be 100 dollars, what premium amount should it charge?
Answe 2 Expected loss = 0 * 0.8 + 1000 * 0.1 + 0.08 * 5000 + 0.02 * 10000 = $700
Expected profit = $100
so premium must be ($700 - $500) + $ 100 = $ 300
Answer Q.3
E[ Max (X,Y) ] = summation of pr(x,y) * Max( x,y) = 0 * 0.06 + 5 *0.09 + 10*0.05 + 5 * 0.07 + 5* 0.19 + 10* 0.23 + 10 * 0.02 + 10 *0.15 + 10* 0.14
= 7.65
=
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