Question

PROBLEM 4. Toss a fair coin 5 times, and let X be the number of Heads. Find P ( X=4 | X>= 4 ).

Answer #1

If we Toss a fair coin 5 times, and let X be the number of Heads

( Number of heads ) | 0 | 1 | 2 | 3 | 4 | 5 |

and

Toss a fair coin for three times and let X be the number of
heads.
(a) (4 points) Write down the pmf of X. (hint: first list all
the possible values that X can take, then calculate the probability
for X taking each value.)
(b) (4 points) Write down the cdf of X.
(c) (2 points) What is the probability that at least 2 heads
show up?

I toss a biased coin 15 times, with a probability of heads: ? =
0.25. Let x equal the number of heads I toss. The probability I
toss at least 2 heads is _________________ (3 points)

A fair coin is flipped 400 times. Let X be the number of heads
resulting, find P[190<= X <= 200]
a) About 34%
b) About 95%
c) About 68%
d) About 25%
e) About 50%

a
fair coin is flipped 44 times. let X be the number if heads. what
normal distribution best approximates X?

Suppose we toss a fair coin twice. Let X = the number of heads,
and Y = the number of tails. X and Y are clearly not
independent.
a. Show that X and Y are not independent. (Hint: Consider the
events “X=2” and “Y=2”)
b. Show that E(XY) is not equal to E(X)E(Y). (You’ll need to
derive the pmf for XY in order to calculate E(XY). Write down the
sample space! Think about what the support of XY is and...

I toss a coin two times. X1 is the number of heads on the first
toss. X2 is the number of heads on the second toss.
Find the mean of X1.
Find the variance of X1.
Find the mean of X1 + X2. (This is the number of heads in 2
tosses.)
Find the variance of X1 + X2.
If you tossed 10 coins, how many heads would you expect? What is
the variance of the number of heads?

A fair coin has been tossed four times. Let X be the number of
heads minus the number of tails (out of four tosses). Find the
probability mass function of X. Sketch the graph of the probability
mass function and the distribution function, Find E[X] and
Var(X).

An unfair coin is such that on any given toss, the probability
of getting heads is 0.6 and the probability of getting tails is
0.4. The coin is tossed 8 times. Let the random variable X be the
number of times heads is tossed.
1. Find P(X=5).
2. Find P(X≥3).
3. What is the expected value for this random variable?
E(X) =
4. What is the standard deviation for this random variable? (Give
your answer to 3 decimal places)
SD(X)...

A coin is tossed five times. Let X = the number of heads. Find
P(X = 3).

A fair coin is tossed three times. Let X be the number of heads
among the first two tosses and Y be the number of heads among the
last two tosses. What is the joint probability mass function of X
and Y? What are the marginal probability mass function of X and Y
i.e. p_X (x)and p_Y (y)? Find E(X) and E(Y). What is Cov(X,Y) What
is Corr (X,Y) Are X and Y independent? Explain. Find the
conditional probability mass...

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