GATE CSE
First time here? Checkout the FAQ!
x
+6 votes
956 views

Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X ≤ -1) = P (Y ≥ 2)$ , the standard deviation of $Y$ is

  1. $3$
  2. $2$
  3. $\sqrt{2}$
  4. $1$
asked in Probability by Veteran (58.2k points)   | 956 views

3 Answers

+11 votes
Best answer

answer = option A

answered by Veteran (27.5k points)  
selected by
open eyes, look what is given in the 1st image.
+9 votes
First lets convert both X and Y to Standard normal distribution.

Z=X-1/2

Z=Y+1/σ

Now replace X and Y in P(X<=-1)=P(Y>=2) we get P(Z<=-1)=P(Z>=3/σ)

Since the Standard Normal Curve is symmetric about the mean( i.e, zero) -(-1)=3/σ⟹σ = 3.

Answer is Option A
answered by Active (2.2k points)  
+1 vote
(A) is the correct answer?
answered by (27 points)  
Top Users Feb 2017
  1. Arjun

    5234 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3828 Points

  4. Aboveallplayer

    3006 Points

  5. Debashish Deka

    2378 Points

  6. sriv_shubham

    2308 Points

  7. Smriti012

    2148 Points

  8. Arnabi

    2008 Points

  9. sh!va

    1672 Points

  10. mcjoshi

    1628 Points

Monthly Topper: Rs. 500 gift card

20,841 questions
26,000 answers
59,638 comments
22,072 users