If an unfair coin comes up heads 60% of the time and tails 40% of the...
If an unfair coin comes up heads 60% of the time and tails 40% of the time, what is the expectation if heads is valued at 1 and tails is valued at -1?
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If an unfair coin comes up heads 60% of the time and tails 40%
of the...
Suppose you have an unfair coin that is weighted so that heads comes up only 30...
Suppose you have an unfair coin that is weighted so that heads comes up only 30 percent of the time. If you flip the coin 4 times, what is the probability that you obtain at least 3 heads in the 4 flips?
A fair coin is repeatedly flipped. The following sequence of heads and tails comes up: HTTHTHHTHHHHH....
A fair coin is repeatedly flipped. The following sequence of heads and tails comes up: HTTHTHHTHHHHH. What is the probability that the next result will be a head? 1/64 1/32 1/2 1/14
A coin comes up heads 75 times and tails 25 times. What is the computed chi-square...
A coin comes up heads 75 times and tails 25 times. What is the computed chi-square value for a χ² goodness-of-fit test that assumes equal heads and tails? Less than 3.841 Between 3.841 and 6.635 Between 6.635 and 10.827 Greater than 10.827
I toss an unfair coin 12 times. This coin is 65% likely to show up heads....
I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Since the binomial table only gives up to 50%, I will have to look at probability for tails. Which column will I be looking in (ie. .05, .30, .50...)?
(a) [15 points] Suppose you have a weighted coin in which heads comes up with probability...
(a) [15 points] Suppose you have a weighted coin in which heads comes up with probability 3/4 and tails with probability 4. If you flip heads you win $2, but if you flip tails, you lose $1. What is the expected value of a coin flip?
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with...
Problem 3.
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It is flipped until two consecutive heads or two consecutive tails occur. Find the expected number of flips 5. Suppose that PX a)p, P[Xb-p, a b. Show that (X-b)/(a-b) is a Bernoulli variable, and find its variance
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It...
A coin that comes up heads with probability p is flipped n consecutive times. What is...
A coin that comes up heads with probability p is flipped n consecutive times. What is the probability that starting with the first flip there are always more heads than tails that have appeared?
Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair...
Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair coin (that is a coin with equal probability of 1. The coin lands 'tails-tails' (that is, a tails is immediately followed by a tails) for the first 2. The coin lands 'tails-heads (that is, a tails is immediately followed by a heads) for the landing heads and tails) is tossed repeatedly until one of the following happens time. In this case Alice wins. first...
What is the probability of tossing an unfair coin 19 times and having heads come up...
What is the probability of tossing an unfair coin 19 times and having heads come up 12 or more times (P(T)=0.7)?
What is the probability of tossing an unfair coin 19 times and having heads come up...
What is the probability of tossing an unfair coin 19 times and having heads come up 12 or more times (P(T) = 0, 7) ?
(a) [15 points] Suppose you have a weighted coin in which heads comes up with probability 3/4 and tails with probability 4. If you flip heads you win $2, but if you flip tails, you lose $1. What is the expected value of a coin flip?
Problem 3.
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It is flipped until two consecutive heads or two consecutive tails occur. Find the expected number of flips 5. Suppose that PX a)p, P[Xb-p, a b. Show that (X-b)/(a-b) is a Bernoulli variable, and find its variance
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It...
Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair coin (that is a coin with equal probability of 1. The coin lands 'tails-tails' (that is, a tails is immediately followed by a tails) for the first 2. The coin lands 'tails-heads (that is, a tails is immediately followed by a heads) for the landing heads and tails) is tossed repeatedly until one of the following happens time. In this case Alice wins. first...
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