Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the function $P[X=x]=\left\{\begin{array}{cc}\frac{K \cdot 2^x}{x !}, & x=0,1,2,3 \\ 0, & \text { otherwise }\end{array}\right.$ Forms p.m.f., then value of $K$ is
MathematicsProbabilityMHT CETMHT CET 2022 (08 Aug Shift 1)
Options:
  • A $\frac{5}{19}$
  • B $\frac{2}{19}$
  • C $\frac{3}{19}$
  • D $\frac{1}{19}$
Solution:
2634 Upvotes Verified Answer
The correct answer is: $\frac{3}{19}$
$\begin{aligned} & \sum P(x)=1 \\ & \Rightarrow k \cdot \frac{2^0}{0 !}+k \cdot \frac{2^1}{1 !}+k \cdot \frac{2^2}{2 !}+k \cdot \frac{2^3}{3 !}=1 \\ & \Rightarrow \frac{19}{3} k=1 \\ & \Rightarrow k=\frac{3}{19}\end{aligned}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.