Question
In: Statistics and Probability
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
Solutions
orchestra answered 1 year agoRelated Solutions
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 10 red balls and 5 green balls. Balls are randomly selected, one at...
An urn contains 10 red balls and 5 green balls. Balls are
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is obtained. What is the probability that exactly k draws are
needed? What is the probability that at least k draws are needed?
Define a random variable associated with this experiment. Determine
its probability mass function and cumulative distribution function,
sketch their graphs. Find the expectation, variance and standard
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An urn contains 7 red and 10 blue balls. If 4 balls are to be randomly...
An urn contains 7 red and 10 blue balls. If 4 balls are to be
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Explain each step ?
Urn 1 contains 10 red balls, 5 green balls and 12 orange. Inside Urn 2 there...
Urn 1 contains 10 red balls, 5 green balls and 12 orange. Inside
Urn 2 there are 7 red, 13 green, and 20 orange balls. Flip a coin
to choose the urn, so there is a 55% chance to heads, you pick urn
1. If you pick tails, you pick urn 2. Then pick a ball from one of
the urns after you flip. If you choose an orange ball, pick again
but do this only once.
a) Draw a...
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 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?
An urn contains 4 red balls and 3 green balls. Two balls are sampled randomly. Let...
An urn contains 4 red balls and 3 green balls. Two balls are
sampled randomly.
Let W denote the number of green balls in the sample when the
draws are done with replacement. Give the possible values and the
PMF of W.
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]
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?
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