Question

In this problem, a fair coin is flipped three times. Assume that a random variable X is defined to be 7 times the number of heads plus 4 times the number of tails.

How many different values are possible for the random variable X?

Answer #1

**Solution:**

Here a fair coin is flipped three times. So the possible value of number of head in the flipping the coin is 0,1,2 and 3

Let H and T denote number of Head and Tail.

When H = 0, T = 3

When H = 1, T = 2

When H = 2, T = 1

When H = 3, T = 0

Here the random varibale, X = 7H + 4T

When H = 0 and T = 3, X = 7*0 + 4*3 = 12

When H = 1 and T = 2, X = 7*1 + 4*2 = 15

When H = 2 and T = 1, X = 7*2 + 4*1 = 18

When H = 3 and T = 0, X = 7*3 + 4*0 = 21

**Hence the possible value of random variable X is 12, 15,
18 and 21.**

1. In this problem, a fair coin is flipped three times. Assume
that a random variable X is defined to be 7 times the number of
heads plus 4 times the number of tails.
How many different values are possible for the random variable
X?
2. Fill in the table below to complete the probability density
function. Be certain to list the values of X in ascending
order.
Value of X | Probability

A coin is flipped. If a heads is flipped, then the coin is
flipped 4 more times and the number of heads flipped is noted;
otherwise (i.e., a tails is flipped on the initial flip), then the
coin is flipped 2 more times and the result of each flip (i.e.,
heads or tails) is noted successively. How many possible outcomes
are in the sample space of this experiment?

As in the previous problem, a fair coin is flipped 28 times. If
X is the number of heads, then the distribution of X can be
approximated with a normal distribution, N(14,2.6), where the mean
(μ) is 14 and standard deviation (σ) is 2.6. Using this
approximation, find the probability of flipping 18 or 19 heads. You
may use the portion of the Standard Normal Table below.
z1.21.31.41.51.61.71.81.92.02.12.20.000.88490.90320.91920.93320.94520.95540.96410.97130.97720.98210.98610.010.88690.90490.92070.93450.94630.95640.96490.97190.97780.98260.98640.020.88880.90660.92220.93570.94740.95730.96560.97260.97830.98300.98680.030.89070.90820.92360.93700.94840.95820.96640.97320.97880.98340.98710.040.89250.90990.92510.93820.94950.95910.96710.97380.97930.98380.98750.050.89440.91150.92650.93940.95050.95990.96780.97440.97980.98420.98780.060.89620.91310.92790.94060.95150.96080.96860.97500.98030.98460.98810.070.89800.91470.92920.94180.95250.96160.96930.97560.98080.98500.98840.080.89970.91620.93060.94290.95350.96250.96990.97610.98120.98540.98870.090.90150.91770.93190.94410.95450.96330.97060.97670.98170.98570.9890

Given a fair coin, if the coin is flipped n times, what is the
probability that heads is only tossed on odd numbered tosses.
(tails could also be tossed on odd numbered tosses)

4. A fair coin is flipped 6 times.
a. what is the distribution
of outcomes?
b. what is the probability
of getting 4 heads/2 two tails in six flips of a
coin?

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

An unfair coin is flipped 3 times, heads is 4 times as likely to
occur than tails.
x= the number of heads.
Find the probability distribution, E(x), and σ(x).

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?

Consider the following three random variables:
a) a coin is repeatedly flipped
Let X= number of tails before the first head
b) a box contains 10 red and 6 white chips. 5 chips are drawn at
rabdom from the box.
Let Y= the number of red chips drawn.
c) A weighted die is rolled 12 times.
Let W= the number of times a "4" is rolled
in each case, decide whether the random variable is
binomial.

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%

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 7 minutes ago

asked 10 minutes ago

asked 11 minutes ago

asked 27 minutes ago

asked 33 minutes ago

asked 35 minutes ago

asked 39 minutes ago

asked 44 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago