# DHS 18.2 - Option 3. Decisions Ryabushko AP

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1. Find the distribution of the said discrete CB X and its distribution function F (x). Calculate the expectation M (X), the variance of D (X) and standard deviation σ (X). Draw the graph of the distribution function F (x)

1.3. The probability of failure-free operation during the warranty period for the TV of the first type is 0.9, the second type - 0.7, the third type - 0.8; SW X - the number of TVs, worked the warranty period, among the three different types of TVs.

2. Dana distribution function F (x) DM X. Find the probability density function f (x), the expectation M (X), the variance of D (X), and the probability of hitting NE X on the interval [a; b]. Construct the graphs of the functions F (x) and f (x).

3. Solve the following problems.
3.3. All values are uniformly distributed NE X lie on the interval [2; 8]. Find the probability of getting into CB X time (3, 5).

4. Solve the following problems.
4.3. The random variable X is the arithmetic average of 3200 independent and identically distributed random variables with mean equal to 3, and a variance equal to 2. Find the probability that X takes the value SV in the interval (2.95; 3.075).