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Probability Gravner 81.a
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Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads.
(a) Assume that you play this game $300$ times. What is, approximately, the probability that you win at least $250$ dollar ?
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Probability Gravner 81.b
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (b) Approximately how many times do you need to play so that you win at least $250$ dollar with probability at least $0.99$.
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Probability Gravner 82.a
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (a) Compute the expectation $EM$.
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Probability Gravner 79.a
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (a) Determine c.
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Probability Gravner 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
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