91Ó°ÊÓ

For the event of rolling one die, find: a. \(P\left(\begin{array}{c}\text { Rolling at } \\ \text { least a } 3\end{array}\right)\) b. \(P\left(\begin{array}{c}\text { Rolling an } \\ \text { odd number }\end{array}\right)\)

Find the value of the constant \(a\) that makes each function a probability density function on the stated interval. \(a x^{2}(1-x)\) on [0,1]

If \(X\) is a uniform random variable on the interval \([0,10],\) find: a. the probability density function \(f(x)\) b. \(E(X)\) c. \(\operatorname{Var}(X)\) d. \(\sigma(X)\) e. \(P(8 \leq X \leq 10)\)

1-10. Find each probability for a standard normal random variable \(Z\). \(P(0 \leq Z \leq 1.95)\)

Find each probability for a standard normal random variable \(Z\). \(P(-1.23 \leq Z \leq 0)\)

For the event of tossing a coin twice, find: a. \(P\left(\begin{array}{c}\text { Tossing exactly } \\ \text { one head }\end{array}\right)\) b. \(P\left(\begin{array}{c}\text { Tossing at most } \\ \text { one head }\end{array}\right)\)

Find the value of the constant \(a\) that makes each function a probability density function on the stated interval. \(a \sqrt{x}\) on [0,1]

If \(X\) is a uniform random variable on the interval \([0,0.01],\) find: a. the probability density function \(f(x)\) b. \(E(X)\) c. \(\operatorname{Var}(X)\) d. \(\sigma(X)\) e. \(P(X \geq 0.005)\)

3-4. For the event of tossing a coin three times, find: a. \(P\left(\begin{array}{c}\text { Tossing exactly } \\ \text { one head }\end{array}\right)\) b. \(P\left(\begin{array}{c}\text { Tossing exactly } \\ \text { two heads }\end{array}\right)\)

Find the value of the constant \(a\) that makes each function a probability density function on the stated interval. \(a x^{2}\) on [0,3]