Tag: random variable and mathematical expectation

Questions Related to random variable and mathematical expectation

Sizes of shoe are which types of variables?

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. discrete

  2. random

  3. continous

  4. nominal

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Correct Option: A
Explanation:

There are two types of variables. Discrete and continuous. 

To explain by example, the set of real numbers is continuous, between any two distinct real numbers there exist infinite real numbers. Between 1.2 and 1.3 there exists 1.24 and so many more. 
The set of natural numbers on the other hand, constitutes a discrete sample space. 
Due to the limitations posed by manufacturing tools, we can only produce shoes of varying sizes in discrete steps.

The mean of discrete obervations $y _1, y _2$ , ................ , $y _n$ is given by

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{n}$

  2. $\displaystyle \frac{\sum _{i=1}^{n} y _i}{\sum _{i=1}^{n}i}$

  3. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{n}$

  4. $\displaystyle \frac{\sum _{i=1}^{n} y _i f _i}{\sum _{i=1}^{n}y _if _i}$

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Correct Option: A
Explanation:

Mean of terms = $\dfrac{Sum}{number}$


Therefore, Mean = $\displaystyle \dfrac{\sum _{i=1}^{n} y _i}{n}$

Number of patients in a hospital are discrete variable


If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $1$

  2. $0$

  3. can't determine

  4. None of these

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Correct Option: A

Distance travelled by a car is a continuous variable
If true then choose $1$ and if false then choose $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $1$

  2. $0$

  3. $4$

  4. none of the above

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Correct Option: A
Explanation:

The distance travelled by a car can be a fraction hence it is a continuous variable

Hence, option (A) is correct

Sizes of shoes are discrete variables,

If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. Varies from case to case

  2. $0$

  3. $1$

  4. None of these

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Correct Option: C
Explanation:

Size of a shoe can have values only in natural numbers. Hence, it is a discrete variable.

Hence, option (C) is correct

A quantity which can vary from one individual to another is called a variable.


If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $0$

  2. $1$

  3. can't determine

  4. None of these

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Correct Option: B
Explanation:

A quantity which can vary from one individual to another is called a variable.

The variable number of children in your class is discrete variable

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. True

  2. False

  3. can't determine

  4. none of these

Show answer
Correct Option: A
Explanation:

Number of children in the class can be counted and it will take value only as a whole number. Hence, it is a discrete variable.

The sizes of shoes is a continuous variable
If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $1$

  2. $0$

  3. $10$

  4. None of these

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Correct Option: B
Explanation:

Size of a shoe can have integer values only. Hence, it is a discrete variable.

Time is continuous variable
If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. $1$

  2. $0$

  3. $3$

  4. None of these

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Correct Option: A
Explanation:

Time can have any value including integers and rational numbers. Hence, it is a continuous variable.

State, which of the following variables are continuous and which are discrete :


Daily temperature of a city is continuous
If true then enter $1$ and if false then enter $0$

business mathematics and statistics random variable and mathematical expectation discrete and continuous data random variable random variable and its types

  1. Can't determine

  2. $0$

  3. $1$

  4. None of these

Show answer
Correct Option: C
Explanation:

Temperature of a city can have any value including integers and rational numbers. Hence, it is a continuous variable.