Question
In: Statistics and Probability
An unbiased coin is tossed four times. Let the random variable X denote the greatest number...
An unbiased coin is tossed four times. Let the random variable X denote the greatest number of successive heads occurring in the four tosses (e.g. if HTHH occurs, then X = 2, but if TTHT occurs, then X = 1).
Derive E(X) and Var(X).
(ii) The random variable Y is the number of heads occurring in the four tosses. Find Cov(X,Y).
Solutions
orchestra answered 1 year agoRelated Solutions
A fair coin is tossed four times. Let X denote the number of heads occurring and...
A fair coin is tossed four times. Let X denote the number of
heads occurring and let Y denote the longest string of heads
occurring. (i) determine the joint distribution of X and Y (ii)
Find Cov(X,Y) and ρ(X,Y).
An honest coin is tossed n=3600 times. Let the random variable Y denote the number of...
An
honest coin is tossed n=3600 times. Let the random variable Y
denote the number of tails tossed. Use the 68-95-99.7 rule to
determine the chances of the outcomes. (A) Estimate the chances
that Y will fall somewhere between 1800 and 1860. (B) Estimate the
chances that Y will fall somewhere between 1860 and 1890.
A coin is tossed three times. X is the random variable for the number of heads...
A coin is tossed three times. X is the random variable for the
number of heads occurring.
a) Construct the probability distribution for the random
variable X, the number of head occurring. b) Find P(x2). c) Find
P(x1). d) Find the mean and the standard deviation of the
probability distribution for the random variable X, the number of
heads occurring.
Q7 A fair coin is tossed three times independently: let X denote the number of heads...
Q7 A fair coin is tossed three times independently: let X denote
the number of heads on the first toss (i.e., X = 1 if the first
toss is a head; otherwise X = 0) and Y denote the total number of
heads.
Hint: first figure out the possible values of X and Y , then
complete the table cell by cell.
Marginalize the joint probability mass function of X and Y in
the previous qusetion to get marginal PMF’s.
1. A coin is tossed 3 times. Let x be the random discrete variable representing the...
1. A coin is tossed 3 times. Let x be the random
discrete variable representing the number of times tails comes
up.
a) Create a sample space for the event;
b) Create a probability distribution table for the discrete
variable
x;
c) Calculate the expected value for x.
2. For the data below, representing a sample of times
(in minutes) students spend solving a certain Statistics problem,
find P35, range, Q2 and IQR.
3.0, 3.2, 4.6, 5.2 3.2, 3.5...
a) A coin is tossed 4 times. Let X be the number of Heads on the...
a) A coin is tossed 4 times. Let X be the number of Heads on the
first 3 tosses and Y be the number of Heads on the last three
tossed. Find the joint probabilities pij = P(X = i, Y = j) for all
relevant i and j. Find the marginal probabilities pi+ and p+j for
all relevant i and j. b) Find the value of A that would make the
function Af(x, y) a PDF. Where f(x, y)...
A coin is tossed 6 times. Let X be the number of Heads in the resulting...
A coin is tossed 6 times. Let X be the number of Heads in the
resulting combination. Calculate the second moment of X.
(A).Calculate the second moment of X
(B). Find Var(X)
1. Suppose four distinct, fair coins are tossed. Let the random variable X be the number...
1. Suppose four distinct, fair coins are tossed. Let the random
variable X be the number of heads. Write the probability mass
function f(x). Graph f(x).
2. For the probability mass function obtained, what
is the cumulative distribution function F(x)? Graph F(x).
3. Find the mean (expected value) of the random variable X given
in part 1
4. Find the variance of the random variable X given in part
1.
A coin is tossed twice. Let Z denote the number of heads on the first toss...
A coin is tossed twice. Let Z denote the number of heads on the
first toss and W the total number of heads on the 2 tosses. If the
coin is unbalanced and a head has a 40% chance of occurring, find
the correlation between W and Z.
A coin is tossed twice. Let Z denote the number of heads on the first toss...
A coin is tossed twice. Let Z denote the number of heads on the
first toss and W the total number of heads on the 2 tosses. If the
coin is unbalanced and a head has a 40% chance of occurring, find
the correlation between W and Z
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