Chapter 3: Problem 9
Toss two nickels and three dimes at random. Make appropriate assumptions and compute the probability that there are more heads showing on the nickels than on the dimes.
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. Let \(X\) and \(Y\) have a bivariate normal distribution with parameters \(\mu_{1}=\) \(\mu_{2}=0, \sigma_{1}^{2}=\sigma_{2}^{2}=1\), and correlation coefficient \(\rho .\) Find the distribution of the random variable \(Z=a X+b Y\) in which \(a\) and \(b\) are nonzero constants.
Find \(P(3.28
Let an unbiased die be cast at random seven independent times. Compute the conditional probability that each side appears at least once given that side 1 appears exactly twice.
Consider a random variable \(X\) of the continuous type with cdf \(F(x)\) and pdf
\(f(x)\). The hazard rate (or failure rate or force of mortality) is defined by
$$
r(x)=\lim _{\Delta \rightarrow 0} \frac{P(x \leq X
A certain job is completed in three steps in series. The means and standard deviations for the steps are (in minutes): $$ \begin{array}{ccc} \hline \text { Step } & \text { Mean } & \text { Standard Deviation } \\ \hline 1 & 17 & 2 \\ 2 & 13 & 1 \\ 3 & 13 & 2 \\ \hline \end{array} $$Assuming independent steps and normal distributions, compute the probability that the job will take less than 40 minutes to complete.
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