The value of a and b so that the following is probability mass function

X: 0 1 2
P(X = x): 3a 3b 4b

with mean 1.1, is:

This question was previously asked in
SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. (0.2, 0.2)
  2. (0.1, 0.1)
  3. (0.1, 0.2)
  4. (0.2, 0.1)

Answer (Detailed Solution Below)

Option 2 : (0.1, 0.1)
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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The correct answer is (0.1,0.1)

Key Points

  • The probability mass function (PMF) of a discrete random variable gives the probabilities associated with each possible value of the random variable. 
  • The mean of a random variable can be calculated by taking the weighted sum of the possible values of the random variable, where the weights are given by the PMF.

 Additional Information

  • The PMF must satisfy the properties of a probability function, i.e. it must be non-negative for all values of the random variable, and the sum of the probabilities over all possible values must equal 1.
  • The mean of a random variable provides a measure of the center of the distribution, and is commonly used in many statistical applications.
  • To determine the PMF given a mean, it is necessary to know the possible values of the random variable, and their probabilities.
  • The mean of a random variable is a parameter of the distribution, and can be used to describe the center of the distribution.
  • The calculation of the mean requires knowledge of the PMF.
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