Probability Control answers, Part 2

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! Are presented in the form of scanned notebook sheet.
Probability theory and mathematical statistics, control, option 5.

1) The plants A and B manufactured and m% n% of all components. From historical data it is known that the plant parts and% b% A and B components of the plant are defective. Randomly selected item was defective.
What is the probability that it is made in the factory A?
Option 5.
a = 5, b = 15, m = 60, n = 40

2) The probability of hitting a target shooter in one shot is equal to p. Find the probability that the target n shots will hit by at least not more than k1 and k2 times.
Option 5.
p = 0.5, k1 = 43, k2 = 57, n = 100

3) Discrete random variable takes the value xi with probability pi. Find it mean and variance.

4) the probability density function of continuous random variable is of the form: f (x) = ye ^ -ax ^ (2 + bx + c)
Find the unknown number m, the distribution function F (x), the expectation of M (x) and the variance of D (x).

5) from the current range of products manufactured distributed random variable X rollers. Find the mean and standard deviation of the distribution of the random variable X - deviation from the nominal diameter of the roller

6) The machine packs up sugar packets. Produced random sample of size n of packets. The average weight of a package of sugar in the sample X kg, the sample standard deviation s kg. Find the confidence interval for the average packet of sugar in the general population with a confidence level of p.

! Are presented in the form of scanned notebook sheet.

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