3 math problems of probability theory

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1. The probability of getting accidentally thrown point to any part of the segment depends on the length of the segment and is proportional to it.

Required:
1) build number and the distribution function of the number of points that fall on the right half of the segment if the segment is thrown 5 points; calculate the mean and variance of the quantity
2) to assess the probability that 5 out of 60 points will get thrown to the selected part of the twentieth segment.

2. The time t after the dissolution of the composition of the hill - a random variable, distributed exponentially. Let λ = 5 - the average number of trains that can slide to disband an hour. Determine the probability that the time of dissolution of the composition will be more than 0.3 hours.

3.Plotnost distribution of two-dimensional random variable (X, Y) has the form:

Required:
1) Find the coefficient A
2) Write an expression for the density distribution of f1 (x) and f2 (y)
3) Calculate the expectations mx and my, standard deviation and σh σu.
4) Install dependent Does X and Y.

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