Question
In: Math
Suppose that 3 balls are chosen from an urn which contains 5 red, 6 white and...
Suppose that 3 balls are chosen from an urn which contains 5
red, 6 white and 10 blue balls. Assume X and Y represents,
respectively, the number of red balls chosen and summation of
chosen red and white balls.
(a) Determine the outcomes, and then represent all possible
outcomes with a chart of X and Y.
(b) Determine pXY [x,y], and then from pXY [x,y] determine, pX[x]
and pY [y].
(c) Determine Cov(X, Y ) and ρXY .
(d) Determine the joint CDF.
Solutions
milcah answered 1 year agoRelated Solutions
An urn contains 4 white balls and 6 red balls. A second urn contains 8 white...
An urn contains 4 white balls and 6 red balls. A second urn
contains 8 white balls and 2 red balls. An urn is selected, and a
ball is randomly drawn from the selected urn. The probability of
selecting the first urn is 0.7. If the ball is white, find the
probability that the second urn was selected. (Round your answer to
three decimal places.)
An urn contains 4 white balls and 6 red balls. A second urn contains 7 white...
An urn contains 4 white balls and 6 red balls. A second urn
contains 7 white balls and 3 red balls. An urn is selected, and the
probability of selecting the first urn is 0.1. A ball is drawn from
the selected urn and replaced. Then another ball is drawn and
replaced from the same urn. If both balls are white, what are the
following probabilities? (Round your answers to three decimal
places.)
- (a) the probability that the urn...
An urn contains 5 white and 8 red balls. Assume that white balls are numbered. Suppose...
An urn contains 5 white and 8 red balls. Assume that white balls
are numbered. Suppose that 3 balls are chosen with replacement from
that urn. Let Yi = 1 if if the ith white ball is
selected and Yi = 0 otherwise, i = 1,2:
Find the EXPECTED VALUE of Yi given
that a) Y2 = 1; b) Y2 = 0.
An urn contains 6 red balls and 4 green balls. Three balls are chosen randomly from...
An urn contains 6 red balls and 4 green balls. Three balls are
chosen randomly from the urn, without replacement.
(a) What is the probability that all three balls are red? (Round
your answer to four decimal places.)
(b) Suppose that you win $20 for each red ball drawn and you
lose $10 for each green ball drawn. Compute the expected value of
your winnings.
An urn contains 6 red balls, 7 white balls, and 8 blue balls. a) If three...
An urn contains 6 red balls, 7 white balls, and 8 blue
balls.
a) If three balls are sampled without replacement, find
probability that all are different colors
b) If three balls are sampled with replacement, find the
probability that are different colors.
c) i n balls sampled with replacement, find probability that all
are red.
d) If nballs sampled with replacement, find the probability that
all are the same color.
An urn contains 5 red balls and 5 blue balls. (a) If 3 balls are selected...
An urn contains 5 red balls and 5 blue balls.
(a) If 3 balls are selected all at once, what is the
probability that 2 are blue and 1 is red?
(b) If 3 balls are selected by pulling out a ball, noting its
color, and putting it back in the urn before the next section,
what is the probability that only the first and third balls drawn
are blue?
(c) If 3 balls are selected one at a...
An urn contains 5 red balls and 6 blue balls. A ball is drawn. If the...
An urn contains 5 red balls and 6 blue balls. A ball is drawn.
If the ball is red, it is kept out of the urn and an additional
blue ball is added to the urn. Then, a second ball is drawn from
the urn. If the ball is blue, then it is put back in the urn and an
additional blue ball is added to the urn. Then a second ball is
drawn from the urn.
If the second...
Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and...
Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.
Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and...
Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.
Suppose that there is a white urn containing two white balls and three red balls and...
Suppose that there is a white urn containing two white balls and
three red balls and there is a red urn containing two white balls
and four red balls. An experiment consists of selecting at random a
ball from the white urn and then (without replacing the first
ball) selecting at random a ball from the urn having the color of
the first ball. Find the probability that the second ball is
red.
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