Determine the value if k that makes the following pdf a vali

Determine the value if k that makes the following pdf a valid one, if possible. Explain your answer.

Solution

If given the distribution is a pdf then sum of all probabilities must be equal to 1.

i.e 3k+4k+2k+k-5k =1i.e., 5k=1

implies k= 1/5=0.2

the given data can be expressed as

f(x)

probability cannot be negative.here the probability of -1 is -1 which is not possinble.

hence given pdf is not a valid pdf.