Question
In: Statistics and Probability
Toss a coin 5 times. Let X denote the number of tails appeared. a. Write down...
Toss a coin 5 times. Let X denote the number of tails appeared. a. Write down the probability mass function of X. b. Write down the cumulative distribution function of X. c. Graph the cumulative distribution function of X. d. Find the expectation of E[X] e. Find the variance Var[X]
Solutions
orchestra answered 1 year agoRelated Solutions
Let X be the number of Heads when we toss a coin 3 times. Find the...
Let X be the number of Heads when we toss a coin 3 times. Find
the probability distribution (that is, the probability function)
for X
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
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 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).
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.
Flip a fair coin 4 times. Let ? and ? denote the number of heads and...
Flip a fair coin 4 times. Let ? and ? denote the number of heads
and tails correspondingly.
(a) What is the distribution of ?? What is the distribution of ?
?
(b) Find the joint PMF. Are ? and ? independent?
(c) Calculate ?(? ?) and ?(X≠?)(d) Calculate C??(?, ? ) and
C???(?, ? )
Coin toss experiment In this experiment, determine the number of heads and tails after flipping a...
Coin toss experiment In this experiment, determine the number of
heads and tails after flipping a coin for 1000 times. Use two
different methods to find number of heads and tails Use for loops
Use vectors in MATLAB. Repeat this experiment to find running
average of flipping a coin for 200 and 2000 times. Plot the running
average for two experiments using subplot functions
Coin toss experiment In this experiment, determine the number of heads and tails after flipping a...
Coin toss experiment
In this experiment, determine the number of heads and tails
after flipping a coin for 1000 times. Use two different methods to
find number of heads and tails:
Use for loops.
Use vectors in MATLAB.
Repeat this experiment to find running average of flipping a
coin for 200 and 2000 times. Plot the running average for two
experiments using subplot functions.
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)...
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