Suppose you are tossing a fair coin. You will keep tossing until you get two consecutive...

Suppose you are tossing a fair coin. You will keep tossing until you get two consecutive
heads. Let, X represents the number of tosses you will need. So the minimum value of X is
two.
(a) Using hand calculation, calculate P[X = 2], P[X = 3], P[X = 4] and P[X = 5].
(b) How to write an R function that keeps tossing the fair coin until two consecutive heads
show up and returns the total number of tosses. (run this function 1000 times)

Expert Solution

milcah answered 6 months ago

in tossing a coin 1024 times we get 460 tails. is this coin fair? use a...

in tossing a coin 1024 times we get 460 tails. is this coin fair? use a significance level equal to 5%

We keep tossing a fair coin n = 106 million times, write down the outcomes: it...

We keep tossing a fair coin n = 106 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers...

We keep tossing a fair coin n=106 million times, write down the outcomes: it gives a...

We keep tossing a fair coin n=106 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i,i + 1,i + 2,i + 3,...,i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? and calculate...

On each turn, bonnie is tossing a fair coin and Clyde is rolling a fair die....

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For which of these coin-tossing scenarios are you most likely to get heads on every toss?...

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Suppose that we flip a fair coin until either it comes up tails twice or we...

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I toss a fair coin 20 times. (a) Calculate the probability of tossing 18 or more...

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