V – variant number in the group list.

Individual task № 2 on probability theory.

Theme:Laws of distribution and numerical characteristics of random variables.

V – variant number in the group list.

Problem 1. In eachof independent trials event occurs with constant probability . Calculate all probabilities , where – is frequency of event . Construct the graph of probabilities . Find the most probable frequency.

Values of parametres calculate with following formulas:

.

Problem 2. In eachof independent trials event occurs with constant probability . Find probability that event occurs:

1) precisely times;

2) less than and more than times;

3) more than times.

; ; ; .

Problem 3. In each of independent trials event occurs with constant probability . Find probability that event occurs:

1) Precisely times;

2) Precisely times;

3) less than and more than times;

4) less than times.

; ; ; ;

; ; .

Problem 4.At telephone station wrong connection occurs with probability . Find probability that among connections takes place:

1) Precisely wrong connections;

2) less than wrong connections;

3) more than wrong connections.

; ; ;* ;

Note, that remainder is the value, left after division (23/5=4*5+3; so, 3 is remainder; 35/5=7*5+0; 0 is remainder; 3/5=0*5+3; 3 is remainder)

; ; .

Problem 5. In eachof independent trials event occurs with constant probability . Find the probability that relative frequency of this event differs from probability no more than on

; ; ; .

Problem 6.The Random variable is set by the distribution law

Find the function of distribution of a random variable ; construct its graph. Calculate , , .

, , ,

, , ,

Problem 7.TheRandom variable is set by a function of probability density

Find function of distribution . Build graphs of ; . Calculate , , , .

,

Problem 8.TheRandom variable is set by distribution function

Find the function of probability density .Build graphs of . Calculate , , , .

Problem 9.random variable is given. Find probability that this random variable accepts value:

1) In an interval ;

2) less than ;

3) more for ;

4) Differs from the average value no more than on .

, ,

, , , ,

Problem 10.It is given:therandom variable and points , on the numerical axis which divide it into six intervals. Find the probability that this random variable accepts value in these intervals.

, , ,

, , , , ,

Date: 2015-12-11; view: 843