The value of k so that following is probability mass function

X:	-2	-1	0	1	2	3
P(X = x):	2k	3k	4k	3k	2k	k

is

The correct answer is 1/15

Key Points

• The sum of all the probabilities is always equal to 1.
• For a discrete random variable X with a probability mass function, the probabilities must sum to 1, which is a requirement for a valid probability distribution. 
  • Hence, the value of k can be determined by setting the sum of all the probabilities equal to 1 and solving for k.
• In this case, the sum of all the probabilities is given by
  • Hence,\( 2k + 3k + 4k + 3k + 2k + k = 1\)
  • ⇒ 15k = 1
  • ⇒\( k = 1/15\)
• A probability mass function is a function that assigns a probability to each value of a discrete random variable.
• The probabilities assigned to the values of a discrete random variable must sum to 1.
• The value of k can be determined by solving for the sum of all the probabilities equal to 1.

 Additional Information

• Once the value of k is determined, the probabilities can be found by multiplying each probability by k. In this case, the probabilities are
• P(X = -2) = 2k = 2/15 
  P(X = -1) = 3k = 3/15 
  P(X = 0) = 4k = 4/15 
  P(X = 1) = 3k = 3/15 
  P(X = 2) = 2k = 2/15 
  P(X = 3) = k = 1/15
• A probability mass function must be a valid probability distribution, meaning that all probabilities must be non-negative and the sum of all probabilities must be equal to 1.
• The value of k can be determined by solving for the sum of all the probabilities equal to 1.
• The probabilities assigned to the values of a discrete random variable provide information about the likelihood of each value of X.