A coin is tossed repeatedly until heads has occurred twice or
tails has occurred twice, whichever...
A coin is tossed repeatedly until heads has occurred twice or
tails has occurred twice, whichever comes first. Let X be the
number of times the coin is tossed. Find:
A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Define (X = number of the toss on
which the first H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function
A coin is flipped repeatedly until either two heads appear in a
row or two tails appear in a row(and then stop). Find the exact
answer for P(two heads in a row appears before two tails in a row)
for a coin with probability p of getting heads.
A coin has a probability of 1/4 for head, and is repeatedly
tossed until
we throw head. The successive results of the toss are independent
of each other.
What is the probability that the first time we throw head after an
odd number of toss?
Hint: Use the law of total probability and consider the event that
the
first toss is head is, and her complement, as conditioning
events.
Correct answer: 3/7
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 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
Suppose that we flip a fair coin until either it comes up tails
twice or we have flipped it six times. What is the expected number
of times we flip the coin?
2. In 200 tosses of a coin, it was observed that 115 Heads and
85 Tails appeared. Test whether this is a fair coin at the = 0.05
level and at the = 0.01 levels.
STAT 2332
#1. A coin is tossed 1000 times, it lands heads 516 heads, is
the coin fair?
(a) Set up null and alternative hypotheses (two tailed).
(b) Compute z and p.
(c) State your conclusion.
#2. A coin is tossed 10,000 times, it lands heads 5160 heads, is
the coin fair?
(a) Set up null and alternative hypotheses (two tailed).
(b) Compute z and p.
(c) State your conclusion.
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)...