Question
In: Statistics and Probability
An urn contains 5 blue, 3 red and 2 blue gemstones and a person is asked...
An urn contains 5 blue, 3 red and 2 blue gemstones and a person is asked to randomly pick 5 of them. Let X1 and X2 denote the blue and red gemstones respectively, find the following:
- E[X1|X2]
- E[3X12X2-X1X2]
- Are X1 and X2 independent?
- Let R be a region given by (X1+X2≤3) , determineP(X1,X2 ϵ R]
Solutions
orchestra answered 1 year agoRelated Solutions
An urn contains 5 blue, 3 red and 2 blue gemstones and a person is asked...
An urn contains 5 blue, 3 red and 2 blue gemstones and a person
is asked to randomly pick 5 of them. Let X1 and
X2 denote the blue and red gemstones respectively, find
the following:
The joint probability mass function (PMF) of X1 and
X2, i.e.,
pX1X2(x1,x2)
Marginal PMFs of X1 and X2, i.e.,
pX1(x1)
and
pX2(x2)
Determine the first order moments of both X1 and
X2
E[X1|X2]
E[3X12X2-X1X2]
Are X1 and X2
independent?
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, 3 orange, and 2 blue balls. Two balls are randomly selected...
An urn contains 5 red, 3 orange, and 2 blue balls. Two balls are
randomly selected simultaneously.
(a) What is the sample space?
(b) Define an RV X as the number of orange balls selected. Show
the map from the sample space to X.
(c) Find the PMF of X.
(d) Find the CDF of X.
i have the solutions can one show how to find the probablity on
4c
1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls. Take out...
1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls.
Take out 3 balls at a random, without replacement. You win $2 for
each green ball you select and lose $3 for each red ball you
select. Let the random variable X denote the amount you win,
determine the probability mass function of X.
2) Each of the 60 students in a class belongs to exactly one of
the three groups A,B, or C. The membership...
An urn contains 4 red, 5 blue, 2 yellow, and 9 green balls. A group of...
An
urn contains 4 red, 5 blue, 2 yellow, and 9 green balls. A group of
5 balls is selected at random without replacement. What is the
probability that the sample contains:
a. atleast one of each color?
b. at most 3 green balls?
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.
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...
An urn has 2 red, 5 white, and 4 blue balls in an urn and two...
An urn has 2 red, 5 white, and 4 blue balls in an urn and two
are drawn one after another without replacement. What is the
probability that the two balls are both red given that they are the
same color?
A bag contains 4 Blue, 5 red and 3 green balls. Debolina is asked to pick...
A bag contains 4 Blue, 5 red and 3 green balls. Debolina is
asked to pick up three balls at random, one by one without
replacement from that bag. If the balls picked up are of same
colour then Debolina will get Rs. 7000, if the balls picked up are
of different colour, then she will get Rs. 9000, but otherwise she
has to pay Rs. 4000.
a) Find the expected gain of Debolina if she plays the game.
b)...
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