TAM310hw12 - 75 in problem 3 compute the probability that...

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TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.12 (Due Tuesday April 22) 1. Let Z be a random variable equal to the sum of the three numbers that appear when three dice are rolled. a. Determine and plot the probability distribution (also referred to in the text as the prob- ability function) for this random variable. b. Compute E(Z) c. Compute E(Z 2 ) d. Compute Var(Z) 2. Let W be a random variable equal to the sum of the 75 numbers that appear when 75 dice are rolled. Without determining the probability distribution: a. Compute E(W) b. Compute Var(W) 3. Let Av 75 be a random variable equal to the average of the 75 numbers that appear when 75 dice are rolled. a. Compute E(Av 75 ) b. Compute Var(Av 75 ) 4. Assuming a normal distribution for the random variable Av
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Unformatted text preview: 75 in problem 3, compute the probability that Av 75 will be between 3.5 and 3.6. 5. The breakdown voltage of a randomly chosen diode of a particular type is known to be normally distributed with mean 40 volts and standard deviation 1.5 volts. (At this voltage the diode turns into a conductor with dire consequences for the associated power supply.) Find the probability that the breakdown voltage lies between 39 and 42 volts. 6. The following function is a candidate for use as a probability density function: f ( x ) = b 1 8 + A x for 0 ≤ x ≤ 2 otherwise a. Find the value of A which makes f ( x ) an acceptable density function. b. Compute the mean of the associated random variable. c. Compute the variance and standard deviation....
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