a. Construct probability distribution for the random experiment of the difference between the results of two fair dice rolled together. Let X be the random variable for the distribution Use the probability distribution to determine the following i. P(X > 1) P(X < 3) iii. P(0 SXS 5)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Question Two (2)
a.
Construct probability distribution for the random experiment of the difference between
the results of two fair dice rolled together. Let X be the random variable for the
distribution
Use the probability distribution to determine the following
i.
P(X > 1)
i.
P(X < 3)
ii.
P(0 S X< 5)
iv.
P(X < 5|X > 0)
V.
P(X > 2|X < 6)
Question Three (3)
a. Semiconductor lasers used in optical storage products require higher power levels for
write operations than for read operations. High-power-level operations lower the useful
life of the laser. Lasers in products used for backup of higher speed magnetic disks
primarily write, and the probability that the useful life exceeds five years is 0.95. Lasers
that are in products that are used for main storage spend approximately an equal amount
of time reading and writing, and the probability that the useful life exceeds five years is
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0.995. Now, 25% of the products from a manufacturer are used for backup and 75°% of
the products are used for main storage. Let A denote the event that a laser's useful life
exceeds five years, and let B denote the event that a laser is in a product that is used for
backup.
Determine the following probabilities
Р (B)
P(A|B)
P(A|B')
P(AN B)
P(AN B')](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe078618-b418-4f70-8fd7-b8344bd8ca1e%2Fa89d71e7-7e25-4ae9-8499-556d4e223000%2Fyufk7ec_processed.jpeg&w=3840&q=75)
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