Question
In: Statistics and Probability
2. In 200 tosses of a coin, it was observed that 115 Heads and 85 Tails...
2. In 200 tosses of a coin, it was observed that 115 Heads and 85 Tails appeared. Test whether this is a fair coin at the = 0.05 level and at the = 0.01 levels.
Solutions
orchestra answered 1 year agoRelated Solutions
A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly (the tosses are independent). Define...
A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Define (X = number of the toss on
which the first H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function
sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30...
sean tosses a coin 40 times and gets 15 heads while Micah tosses
a coin 30 times and gets 16 heads. Suppose that the outcomes of
sean's coin tosses are iid random variable with probability p1 of
getting heads on each toss while Micah’s outcomes are also iid with
a potentially different probability p2 of getting heads.
(1) Calculate the maximum likelihood and method of moments
estimators of p1.
(2) Show that the MLE of p1 is an MVUE for...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.43. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
Find the probability of getting 8 heads in 12 tosses of a coin.
Find the probability of getting 8 heads in 12 tosses of a
coin.
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the
proportion of heads was found to be 0.43. However, the margin of
error for the estimate on the proportion of heads in all tosses was
too big. Suppose you want an estimate that is in error by no more
than 0.03 at the 95% confidence level.
(a) What is the minimum number of tosses required to obtain
this type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion
of heads was found to be 0.61. However, the margin of error for the
estimate on the proportion of heads in all tosses was too big.
Suppose you want an estimate that is in error by no more than 0.03
at the 95% confidence level. (a) What is the minimum number of
tosses required to obtain this type of accuracy? Use the prior
sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion
of heads was found to be 0.61. However, the margin of error for the
estimate on the proportion of heads in all tosses was too big.
Suppose you want an estimate that is in error by no more than 0.04
at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p.
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.
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