Question

An experiment consists of tossing a coin 6 times. Let *X*
be the random variable that is the number of heads in the outcome.
Find the mean and variance of *X*.

Answer #1

Consider an experiment of tossing two coins three times. Coin A
is fair but coin B is not with P(H)= 1/4 and P(T)= 3/4. Consider a
bivariate random variable (X,Y) where X denotes the number of heads
resulting from coin A and Y denotes the number of heads resulting
from coin B.
(a) Find the range of (X,Y)
(b) Find the joint probability mass function of (X,Y).
(c) Find P(X=Y), P(X>Y), P(X+Y<=4).
(d) Find the marginal distributions of X and...

Consider a statistical experiment of flipping a fair coin and
tossing a fair dice simultaneously. Let X be the number heads in
flipping the coin, Y be the number shown in tossing the dice, and Z
= XY. What is the correlation coefficient of X and Y?

Suppose a coin is tossed three times and let X be a random
variable recording the number of times heads appears in each set of
three tosses. (i) Write down the range of X. (ii) Determine the
probability distribution of X. (iii) Determine the cumulative
probability distribution of X. (iv) Calculate the expectation and
variance of X.

An experiment consists of tossing a coin three times and record
the outcomes.
a. Draw a probability tree illustrating all the possible
outcomes of this experiment.
b.What is the probability of at least one tail when tossing
three coins?

A coin is tossed 5 times. Let the random variable ? be the
difference between the number of heads and the number of tails in
the 5 tosses of a coin. Assume ?[heads] = ?.
Find the range of ?, i.e., ??.
Let ? be the number of heads in the 5 tosses, what is the
relationship between ? and ?, i.e., express ? as a function of
??
Find the pmf of ?.
Find ?[?].
Find VAR[?].

Using R, simulate tossing 4 coins as above, and compute the
random variable X(the outcome of tossing a fair coin 4 times &
X = num of heads - num of tails.). Estimate the probability mass
function you computed by simulating 1000 times and averaging.

1. what is a “random variable”. 2. An experiment consists of
flipping 5 fair coins. Let X be the random variable that counts the
number of coins that land heads up. (a) If the experiment ends with
the outcome (HTHHT) then what is the value of X? (b) What is P(X =
1)? (c) What are all the possible values/outputs of X?

Find the probability of each of the following events:
(i) Tossing a coin 5 times with the outcome of five heads.
(ii) Tossing four coins with the outcome of two heads and two
tails in any order.

A coin is tossed 4 times. Let X be the number of times the coin
lands heads side up in those 4 tosses.
Give all the value(s) of the random variable, X. List them
separated commas if there is more than one.
X =

Language: Python
Write a program to simulate an experiment of tossing a fair coin
16 times and counting the number of heads. Repeat this experiment
10**5 times to obtain the number of heads for every 16 tosses; save
the number of heads in a vector of size 10**5 (call it
headCounts).
You should be able to do this in 1-3 lines of numpy code. (Use
np.random.uniform1 to generate a 2d array of 10**5 x 16 random
numbers between 0 and...

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