Homework 2 and 3 in higher mathematics

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Uploaded: 29.08.2013
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Random variables
Homework 2
Objective 1.
In each of the two halves of a football match with both teams scoring three goals with probability 0.2, two goals - with a probability of 0.1, one goal - with a probability of 0.3 and 0.4 with the probability of not scoring any goals. For a random variable X - the number of goals scored in the game - to find p (X <4).
Objective 2.
Shooter carries two shots at a target consisting of three concentric circles. For getting into the center circle of arrows gets three points in the surrounding ring - two and hit the outer ring - one point. The probability of hitting the target in these parts are, respectively, 0.1, 0.3 and 0.4. For a random variable X - number of points - to find F (5).
Task 3.
The density distribution of a continuous random variable X.
Find.
Task 4.
During the relay biathlon each participant is required to hit on the firing line 5 targets, having to do 7 rounds. Chance to hit each shot is 0.8. Find the expectation of a random variable X - the number of affected targets.
Task 5.
Find the expected number of heads with three throws of the coin.
Task 6.
Find the expected number of targets affected after five rounds if the probability of hitting in one shot is 0.4.
Target 7.
Find the variance of precipitation at two sixes dice throws.
Target 8.
In each of the three periods of a hockey match, scoring two goals with probability 0.5, one goal - with a probability of 0.2 and 0.3 with the probability of not scoring any goals. Find the variance of the random variable X - the number of goals scored by a team in the match.
Elements of linear programming

Homework 3
Objective 1.
Find using graphical method the maximum of
with restrictions

Objective 2.
Find using graphical method minimum of
with restrictions

Task 3.
Find using the simplex method the maximum of
with restrictions

Task 4.
Trading company for the sale of goods of three types (A, B, C) uses the resources: staff time and area salesrooms. Profits from the sale of a consignment of the form A - $ 5, type B - 8 USD, type C - 6 USD To determine the optimal structure of trade, for maximum profit. The overhead of one consignment sale of each type are shown in the table.
Resource Product type Volume of resources
A B C
Time, man-hours 0.5 0.7 0.6 370
Area, m2 0.1 0.3 0.2 90

Additional information

The exact formulation of the tasks you can see in the attached image

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