Question
In: Math
Flip a fair coin 4 times. Let ? and ? denote the number of heads and...
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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 ? ?
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(b) Find the joint PMF. Are ? and ? independent?
(c) Calculate ?(? ?) and ?(X≠?)(d) Calculate C??(?, ? ) and C???(?, ? )
Solutions
milcah answered 1 year agoRelated Solutions
Flip a fair coin 100 times. Let X equal the number of heads in the first...
Flip a fair coin 100 times. Let X equal the number of heads in
the first 65 flips. Let Y equal the number of heads in the
remaining 35 flips.
(a) Find PX (x) and PY (y).
(b) In a couple of sentences, explain whether X and Y are or are
not independent?
(c) Find PX,Y (x, y).
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).
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.
A fair coin is tossed r times. Let Y be the number of heads in these...
A fair coin is tossed r times. Let Y be the number of heads in
these r tosses. Assuming Y=y, we generate a Poisson random variable
X with mean y. Find the variance of X. (Answer should be based on
r).
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)...
HOMEWORK-You flip a coin FOUR times. Let H = Number of Heads. Calculate: (a) P (H...
HOMEWORK-You flip a coin FOUR times. Let H = Number of
Heads.
Calculate:
(a) P (H = 4) =
(b) P (H ≥ 1) =
(c) P (H < 4) =
(d) P (1 < H ≤ 4) =
HINT: GET YOUR SAMPLE SPACE.
Leave your answers EITHER as a simplified fraction ( e.g. 4/16 =
1/4 when simplified) OR a decimal rounded to FOUR
decimal places. Also do not forget to enter your leading zero when
entering decimals.
CAUTION: FOLLOW...
Every day you flip a fair coin four times and if it is heads all four...
Every day you flip a fair coin four times and if it is heads all
four times, you give a dollar to charity. In a year with 365 days,
what is your expected annual donation to charity and what is the
variance?
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
1. Flip a fair coin ten times. Find the probability of at least seven heads. 2....
1. Flip a fair coin ten times. Find the probability of at least
seven heads.
2. Draw five cards at once from a deck. Find the probability of
getting two pairs.
3. Roll a die infinitely times. Find the probability that you
see an even number before you see an one.
4. You and your friend take turns to draw from an urn containing
one green marble and one hundred blue marbles, one at a time and
you keep the...
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