1. In each of the two bins shows eight black and two white ball. From the second ballot boxes randomly shifted first one ball, then removed from the first urn at random one ball. Find the probability that the excavated from the first ball of the urn will be black.
2. The distribution of a discrete random variable X is given in the table, the first row shows the possible values \u200b\u200bof the random variable X, and the second line the probability of possible values. Find the expectation, variance and standard deviation of the random variable X.


30 40 50 60 70

0.1 0.2 0.5 0.1 0.1
3. Set the continuous random variable X distribution function F (x). Requires 1) to find the probability density function f (x). 2) build a schematic drawing F (x), f (x). 3) Find the mean and variance of X.
4. Set the expectation and standard deviation of a normally distributed random variable X. Write probability density and schematically construct its graph, find the probability that X takes a value in the interval
,,,,
5. Set the standard deviation of a normally distributed random variable X, the sample mean and the sample size. Find the confidence interval for the estimate of the expectation of the unknown and with given reliability,
6. The inspection of containers revealed that the number of articles damaged during transport and unloading is the empirical distribution, tabulation, where - the number of damaged goods in a single container - the frequency of the event, ie, the number of containers containing the damaged items. It requires at a significance level to test the hypothesis that a random variable X is distributed according to the Poisson law. Use the Pearson's chi-squared test (χ2). .

0 1 2 3 4 5 6

99 67 25 5 2 1 1