# Academy of Management and Finance, St. Petersburg. KR-2

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# Description

The solution of problems of control work-2 in mathematics for students of correspondence courses, specialties: finance and credit, accounting, analysis and audit, management organizations, public municipal management. Option-4 (students whose last digit Gradebook: 4, 6, 8)

E-book (DjVu-file) contains 16 solutions control work assignments for students of the St. Petersburg Academy of Management and Finance. Solving problems presented in the form of a scanned handwriting collected into a single document of 20 pages. This document is stored in a format DjVu, which is open in Internet Explorer after installing utility program (plug-in). Link to download and install DjVu-plugin can be found on the company's homepage LIZARDTECH. DjVu-file that contains the conditions of tasks and their detailed solution completely and ready for viewing on your computer and print. All tasks were successfully offset by teachers of the St. Petersburg Academy of Management and Finance.

A. Random events and discrete random variables.

Task I. Calculate A_12 ^ 2; A_12 ^ 4; C_7 ^ 6; C_6 ^ 2; P_3; P_8.

Quest II. Given: P (AB) = 0,4; R_B (A) = 2/3; R_A (B) = 3/4. Find P (A), P (B) P (A + B) and find out whether the events are dependent A, B?

Quest III. Five randomly machines arranged in a column. Find the probability that the two specific machines will be: a) close; b) at the beginning of the column.

Quest IV. The dash has five guns, hit probability of which are, respectively, 0.5; 0.6; 0.7; 0.8 and 0.9. Find the probability of hitting in one shot if shooting takes one of the guns at random.

Quest V. The family of four children. Assuming that the probability of having a boy is 0.5, find the probability that among these children:
a) there is at least one boy; b) at least two boys.

Quest VI. The probability that a subscriber will call the PBX for an hour, the same for all subscribers and is equal to 0.01. ATS serves 200 subscribers. Get the probability that for an hour followed by the PBX: a) at least two rings; b) at least one call.
What is the most probable number of calls to the PBX for an hour?

Quest VII. For a discrete random variable X with the next distribution: a) make a series of distributions of random variables
Y = X-1 and Z = max {X; 0};
b) Calculate the mean and variance of the random variable Z;
c) plot the distribution function of the random variable X.

Quest VIII. The duration of long-distance calls is distributed approximately exponentially, on average conversation lasts 3 minutes. What is the probability that the next call will be longer than 3 minutes? What part of all conversations lasting less than a minute?

Quest IX. Consider several different operations (Q1, Q2, Q3) with random income. Calculate for all operations expected revenue - Q, standard deviation (SD) - r. Apply these characteristics into a single figure, a graphical image operations. With weighting formula E (Q, r) = 4Q-r Find the best and the worst operation.

B. The continuous random variables, random variables and system
Mathematical Statistics.

I. Setting the random variable Y has a normal distribution with mean equal to two, and the standard deviation equal to one. Let X = 2Y + 5. Find the probability P (X> 10), P (2 <x <5), P (X <2), P (X = 3). Write a function of the density and distribution for the X and build their exemplary graphics. How does it look for SV X usually "three sigma"?

Quest II. Every twentieth loan is not returned on time. This year the bank plans to issue about 300 loans. Find the probability that only a maximum of 10 credits will not be returned in time.