In a sequence of independent flips of a fair coin, let N denote the number of...

In a sequence of independent flips of a fair coin, let N denote the number of flips until there is a run of three consecutive heads. Find P(N ≤ 8). (Should write out transition matrix.)

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orchestra answered 1 year ago

In a sequence of independent flips of a fair coin thwr comes up heads with probability...

In a sequence of independent flips of a fair coin thwr comes up heads with probability 0.6, what is the probability that there is a run of three consecutive heads within the first 10 flips? Show a Markov chain that counts the number of consecutive heads attained.

A fair coin is flipped until a head appears. Let the number of flips required be...

A fair coin is flipped until a head appears. Let the number of flips required be denoted N (the head appears on the ,\1th flip). Assu1ne the flips are independent. Let the o utcon1es be denoted by k fork= 1,2,3, . ... The event {N = k} 1neans exactly k flips are required. The event {,v;;, k} n1eans at least k flips are required. a. How n1any o utcon1es are there? b. What is Pr[N = k] (i.e., the probability...

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???(?, ? )

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...

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You roll two fair four-sided dies and then flip a fair coin. The number of flips...

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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.

Let τ (n) denote the number of positive divisors of n and σ(n) denote the sum...

Let τ (n) denote the number of positive divisors of n and σ(n) denote the sum of the positive divisors of n (as in the notes). (a) Evaluate τ (1500) and σ(8!). (b) Verify that τ (n) = τ (n + 1) = τ (n + 2) = τ (n + 3) holds for n = 3655 and 4503. (c) When n = 14, n = 206 and n = 957, show that σ(n) = σ(n + 1).

Let discrete random variable X be the number of flips of a biased coin required to...

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A fair coin is flipped six times. The outcomes of the coin flips form a palindrome...

A fair coin is flipped six times. The outcomes of the coin flips form a palindrome if the sequence of T’s and H’s reads the same forwards and backwards, e.g. THTTHT. Let A denote the event that the first, second and fourth flips are all ‘T’. Let Z denote the event that the six flips form a palindrome. (a) Is A independent of Z? (b) Is A independent of Z? (c) A fair coin flipped six times and a certain...

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