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Q1 : Consider the following probability distribution function for a continuous random variable:
f(x) = 3x2 /35 -2< x < 3
= 0 elsewhere
(a) Show that this function satisfies the requirements of a probability distribution function.
(b) Calculate the expected (mean) value of x.
(c) Calculate the variance and the standard deviation of x.
Q2: In Problem 6.20, calculate the probability of the following cases:
(a) X ≤ 0.
(b) 0 < x ≤ 1.
(c) x = 2,
Q3: In the manufacturing of an electronic part, the probability of a part being defective is S% (a) What are the probabilities that, in a batch of 100 parts,
• 2 will be defective?• 5 will be defective?• 10 will be defective?
Alice and Bob agree to meet at the bus stop between 12 noon and 1pm. They each arrive at a random time in that interval and wait for 5 minutes before leaving, unless they see the other person. What is the probability that they meet each other?
a professor gives tests that are either hard medium or easy. if she gives a hard test her next test will be either
the compressive strengths of a random sample of 64 specimens of an alloy yielded sample average strength of 5566 psi
He asks you to develop a proposal for the study and submit it to him. Develop the management-research question hierarchy that will help you to develop a specific proposal.
question records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed
The waiting room for jury selection has 40 women and 30 men to choose from. A jury of 12 is selected from these 70 people, what is the probability that exactly 5 of the jury members will be women?
a standard 52-card deck is shuffled and 2 cards are picked without replacement from the top of the deck. the
the following paired samples have been obtained from normally distributed populations. construct a 90 confidence
Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations of X and Y.
a population has u100 and sigma20. if you select a single score from this populaton on the average how close woud it be
Consider babies born in the "normal" range of 37 - 43 weeks gestational age. Extensive data supports the assumption that for such babies born in the United States, birth weight is normally distributed with mean = 3432 grams and standard deviati..
You are appraising the quality of diamonds for your importer. A diamond without a clear center (opaque center) shall be downgraded and sold at discount.
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