HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Ganesh owns a godown used to store electronic gadgets like refrigerator (x) and microwave (y). If the godown can accommodate at most 75 gadgets, then this can be expressed as a constraint by ______

Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______

Choose the correct alternative:

The assignment problem is generally defined as a problem of ______

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Assignment Problem is special case of ______

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When an assignment problem has more than one solution, then it is ______

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The assignment problem is said to be balanced if ______

If the given matrix is ______ matrix, the assignment problem is called balanced problem

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

State whether the following statement is True or False:

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

State whether the following statement is True or False: 

In assignment problem each worker or machine is assigned only one job

X : is number obtained on upper most face when a fair die is thrown then E(X) = ______

The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.

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For the Poisson distribution ______

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A distance random variable X is said to have the Poisson distribution with parameter m if its p.m.f. is given by P(x) = `("e"^(-"m")"m"^"x")/("x"!)` the condition for m is ______

State whether the following statement is True or False:

X is the number obtained on upper most face when a die is thrown, then E(x) = 3.5

State whether the following statement is True or False:  

A discrete random variable X is said to follow the Poisson distribution with parameter m ≥ 0 if its p.m.f. is given by P(X = x) = `("e"^(-"m")"m"^"x")/"x"`, x = 0, 1, 2, .....

State whether the following statement is True or False:

If n is very large and p is very small then X follows Poisson distribution with n = mp

The probability that a bomb will hit the target is 0.8. Using the following activity, find the probability that, out of 5 bombs, exactly 2 will miss the target

Solution: Let p = probability that bomb miss the target

∴ q = `square`, p = `square`, n = 5.

X ~ B`(5, square)`, P(x) = `""^"n""C"_x"P"^x"q"^("n" - x)`

P(X = 2) =  `""^5"C"_2  square = square`

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, using the following activity find the value of m.

Solution: X : Follows Poisson distribution

∴ P(X) = `("e"^-"m" "m"^x)/(x!)`, P(X = 1) = 0.4 and P(X = 2) = 0.2

∴ P(X = 1) = `square` P(X = 2).

`("e"^-"m" "m"^x)/(1!) = square ("e"^-"m" "m"^2)/(2!)`,

`"e"^-"m" = square  "e"^-"m" "m"/2`, m ≠ 0

∴ m = `square`