Question

(a)Assuming that we toss a in-balanced coin for 100 times, and
we get 40 heads from our experiment. Assuming that the relative
frequency is just the true probability for tossing to get a head.
Then we want to know:

Probability for getting a head:

Expected variance if tossing 70 times:

(b)Given a poisson distribution with expectation 4, so the standard
deviation of this distribution should be

Answer #1

Toss a coin three times or toss three coins simultaneously, and
record the number of heads. Repeat the binomial experi- ment 100
times and compare your relative frequency distribution with the
theoretical probability distribution.

a) Suppose we toss a fair coin 20 times. What is the probability
of getting between 9 and 11 heads?
b) Suppose we toss a fair coin 200 times. What is the
probability of getting between 90 and 110 heads?

Suppose you toss an unfair coin 8 times independently. The
probability of getting heads is 0.3. Denote the outcome to be 1 if
you get heads and 0 if you get tails.
1.Write down the sample space.
2. What is the probability of the event that you get a head or a
tail at least once?
3. If you get 8 same toss you will get x dollars, otherwise you
will lose one dollar. On average, how large should x...

Let N = the number of the tossing a coin when we get the first
HEAD. M = the number of the tossing a coin when we get the second
HEAD. We assume probability of getting a HEAD is p. Find the
Probability Distribution of N and M and are they independent?

Let N = the number of the tossing a coin when we get the first
HEAD. M = the number of the tossing a coin when we get the second
HEAD. We assume probability of getting a HEAD is p. Find the
Probability Distribution of N and M and are they independent?

Let N = the number of the tossing a coin when we get the first
HEAD. M = the number of the tossing a coin when we get the second
HEAD. We assume probability of getting a HEAD is p. Find the
Probability Distribution of N and M and are they independent?

Binomial distribution:
a) We know that the probability of getting three heads in three
throws on a weighted coin is 0.008, what is the probability of
getting exactly two heads in three throws of that coin?
b) A bag has 40 red coins and 60 blue coins. We know that the
probability of getting a head on a red coin is 0.5 and getting a
head on a blue coin is 0.3. If we take out a coin from the...

A fair coin is tossed three times. What is the probability
that:
a. We get at least 1 tail
b. The second toss is a tail
c. We get no tails.
d. We get exactly one head.
e. You get more tails than heads.

Suppose we toss a fair coin three times. Consider the events
A: we toss three heads, B: we toss at least one
head, and C: we toss at least two tails.
P(A) = 12.5
P(B) = .875
P(C) = .50
What is P(A ∩ B), P(A ∩ C) and P(B ∩ C)?
If you can show steps, that'd be great. I'm not fully sure what
the difference between ∩ and ∪ is (sorry I can't make the ∪
bigger).

Suppose you toss a coin 100 times. Should you expect to get exactly
50 heads? Why or why not?
A. Yes, because the number of tosses is even, so if the coin
is fair, half of the results should be heads.
B. No, because the chance of heads or tails is the same, the
chance of any number of heads is the same.
C. No, there will be small deviations by chance, but if the
coin is fair, the result...

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