(33 intermediate revisions by the same user not shown)
Line 1: Line 1:
Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
+
Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> has a Poisson distribution with mean $3$. What is the probability of observing fewer than 3 cars during any given minute in this interval?
  
</div>
+
(A) $8/(2e^{3})$
<div class="options">
 
<div class="option">
 
<input type = "radio"  name="2" value="A" onclick="handleOption(this);">          (A) $8/(2e^{3})$
 
  
</div>
+
(B) $9/(2e^{3})$
<div class="option">
 
<input type = "radio"  name="2" value="B" onclick="handleOption(this);">(B) $9/(2e^{3})$
 
  
</div>
+
'''(C) $17/(2e^{3})$'''
<div class="option">
 
<input type = "radio"  name="2" value="C" onclick="handleOption(this);">                                    (C) $17/(2e^{3})$
 
  
</div>
+
(D) $26/(2e^{3})$
<div class="option">
 
<input type = "radio"  name="2" value="D" onclick="handleOption(this);">                                    (D) $26/(2e^{3})$
 
  
 +
==={{Template:Author|Arjun Suresh|{{arjunweb}} }}===
 +
Poisson Probability Density Function (with mean $\lambda$) = $\lambda^{k} / (e^{\lambda}k!)$,
  
</div>
+
We have to sum the probability density function for $k = 0,1$ and $2$ and $\lambda$ = 3 (thus finding the cumulative mass function)
<div class="nooption">
+
 
<input type = "radio"  name="2" value="E" checked = "checked" onclick="handleNooption(this);"> Unmarked
+
=$(1/e^3) + (3/e^3) + (9/2e^3)$
</div>
+
 
<div class="checklater">
+
=$17/(2e^{3})$
<button type="button" name="2" onclick="handleMarkme(this);">Check later </button>
+
 
</div>
+
 
</div>
+
{{Template:FBD}}
</div>
+
 
 +
 
 +
 
 +
[[Category: GATE2013]]
 +
[[Category: Probability questions from GATE]]

Latest revision as of 11:53, 15 July 2014

Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> has a Poisson distribution with mean $3$. What is the probability of observing fewer than 3 cars during any given minute in this interval?

(A) $8/(2e^{3})$

(B) $9/(2e^{3})$

(C) $17/(2e^{3})$

(D) $26/(2e^{3})$

Solution by Arjun Suresh

Poisson Probability Density Function (with mean $\lambda$) = $\lambda^{k} / (e^{\lambda}k!)$,

We have to sum the probability density function for $k = 0,1$ and $2$ and $\lambda$ = 3 (thus finding the cumulative mass function)

=$(1/e^3) + (3/e^3) + (9/2e^3)$

=$17/(2e^{3})$




blog comments powered by Disqus
Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

</div>

<input type = "radio" name="2" value="A" onclick="handleOption(this);"> (A) $8/(2e^{3})$

<input type = "radio" name="2" value="B" onclick="handleOption(this);">(B) $9/(2e^{3})$

<input type = "radio" name="2" value="C" onclick="handleOption(this);"> (C) $17/(2e^{3})$

<input type = "radio" name="2" value="D" onclick="handleOption(this);"> (D) $26/(2e^{3})$


<input type = "radio" name="2" value="E" checked = "checked" onclick="handleNooption(this);"> Unmarked

<button type="button" name="2" onclick="handleMarkme(this);">Check later </button>

</div>