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Q.9 **The number of times a batter gets to bat in a game
follows a binomial distribution N ∼ Binomial(6, 0.8). Given the
number of times N = n that the better has at bat, the number of
hits he gets conditionally follows a binomial distribution as well,
(X|N = n) ∼ Binomial(n, 0.3)**

(a) Find E[X]

(b) Find Var[X]

(c) Find Cov[X, N]

(d) Find ρ[X, N]

Answer #1

a player pays $2 to toss a coin 3 times. He gets $1 if the
number of tails is 2, and he gets $6 if the number of tails is 3,
but nothing otherwise. Let X be his reward based on the number of
tails.
1)What is the expected value of X?
2)What is his expected profit per game?
3)what is Var(X)?

A baseball player, Mickey, who bats 310 (or .310) gets an
average of 3.1 hits in ten at bats. We will assume that each time
Mickey bats he has a 0.31 probability of getting a hit. This means
Mickeys at bats are independent from one another. If we also assume
Mickey bats 5 times during a game and that x= the number of hits
that Mickey gets then the following probability mass function,
p(x), and cumulative distribution function F(x) are...

A baseball player, Mickey, who bats 310 (or .310) gets an
average of 3.1 hits in ten at bats. We will assume that each time
Mickey bats he has a 0.31 probability of getting a hit. This means
Mickeys at bats are independent from one another. If we also assume
Mickey bats 5 times during a game and that x= the number of hits
that Mickey gets then the following probability mass function,
p(x), and cumulative distribution function F(x) are...

Please use excel
b. A rookie is brought to a baseball club on the assumption that
he will have a .300 batting average. (Batting average is the ratio
of the number of hits to the number of times at bat.) In the first
year, he comes to bat 300 times and his batting average is .267.
Could such a low average be considered just bad luck or should he
be sent back to the minor leagues? Assume that his at...

1. Suppose the number of radios in a household has a
binomial distribution
with parameters n = 7, and p = 50 %.
Find the probability of a household having:
(a) 3 or 5 radios
(b) 3 or fewer radios
(c) 3 or more radios
(d) fewer than 5 radios
(e) more than 3 radios
2. A baseball player has a lifetime batting average of 0.228.
If, in a season, this player has 225 "at bats", what is the
probability...

Please show all your work and please answer all the questions.
It is greatly appreciated with a thumbs up. Thank you!
11. Calculate the Binomial mean if n=40, and q= 0.73.
12. Calculate the Binomial standard deviation if n=36 and
'p=0.45.
13. Basketball player Darby Missalot makes a free throw 75% of
the time. What are the chances he will sink his first basket on the
3rd or 4th attempt?
14. The average number of speeding tickets written per year...

The unfair coin (p=Prob(head)=0.3, q=Prob(tail)=1-p=0.7) is
tossed 100 times. Find the probability that number
of heads is between 45 to 50
(both inclusive)
a) Use direct calculation (binomial)
b) Use normal approximation
Using Ti-34 calculator
Equations/answer written out using
binomcdf(x,x,x)
Binompdf(x,x,x)
Invnorm
InvT
tcdf
If possible/needed to solve the equation

The probability of a man hitting the target at a shooting range
is 1/4. If he shoots 30 times, what is the probability that he hits
the target at least 10 times? (Copy your R code and the
result).
Suppose X follows a Chi-square distribution with
degree of freedom 12. Find the cutoff point a, such that, P(X<a)
= 0.85.
Entry to a certain University is determined by a national test.
The scores on this test are normally distributed with a mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

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