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Recent questions tagged expectation
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Expectation : Self Doubt
There is a bag containing 5 white and 5 black balls. You repeat the following experiment till you see a white ball : take a ball uniformly at random out of the bag. If it is white, stop. Otherwise, put it back in the bag. What is the expected number of times you will need to draw a ball from the bag ?
asked
Jun 19
in
Probability
by
suparna kar
(
12
points)

92
views
discrete_maths
expectation
0
votes
0
answers
GATE201412 Video Solution
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

3
views
gate20141
probability
uniformdistribution
expectation
numericalanswers
normal
videosolution
0
votes
0
answers
GATE2005IT32 Video Solution
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

2
views
gate2005it
probability
binomialdistribution
expectation
normal
videosolution
0
votes
0
answers
GATE201324 Video Solution
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\dfrac{1}{2}.$ What is the expected number of unordered cycles of length three? $\dfrac {1}{8}$ $1$ $7$ $8$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate2013
probability
expectation
normal
videosolution
0
votes
0
answers
GATE2017248 Video Solution
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

2
views
gate20172
expectation
poissondistribution
numericalanswers
probability
videosolution
0
votes
0
answers
GATE200480 Video Solution
A point is randomly selected with uniform probability in the $XY$ plane within the rectangle with corners at $(0,0), (1,0), (1,2)$ and $(0,2).$ If $p$ is the length of the position vector of the point, the expected value of $p^{2}$ is $\left(\dfrac{2}{3}\right)$ $\quad 1$ $\left(\dfrac{4}{3}\right)$ $\left(\dfrac{5}{3}\right)$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate2004
probability
uniformdistribution
expectation
normal
videosolution
0
votes
0
answers
GATE201118 Video Solution
If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then $R=0$ $R<0$ $R\geq 0$ $R > 0$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate2011
probability
randomvariable
expectation
normal
videosolution
0
votes
0
answers
GATE19991.1 Video Solution
Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true? There is a sample point at which $X$ has the value $5$. There is a sample point at which $X$ has value greater than $5$. There is a sample point at which $X$ has a value greater than equal to $5$. None of the above
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate1999
probability
expectation
easy
videosolution
0
votes
0
answers
GATE2006IT22 Video Solution
When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ ... $\dfrac{1}{(1  p)}$ $\dfrac{1}{p^{2}}$ $\dfrac{1}{(1  p^{2})}$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

2
views
gate2006it
probability
binomialdistribution
expectation
normal
videosolution
0
votes
0
answers
GATE200474 Video Solution
An examination paper has $150$ multiple choice questions of one mark each, with each question having four choices. Each incorrect answer fetches $0.25$ marks. Suppose $1000$ students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is $0$ $2550$ $7525$ $9375$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate2004
probability
expectation
normal
videosolution
0
votes
0
answers
GATE200618 Video Solution
We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2}$ . The expected value of the smallest number in sample $S$ is: $\left(\frac{1}{n}\right)$ $2$ $\sqrt n$ $n$
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate2006
probability
expectation
normal
videosolution
0
votes
0
answers
GATE201422 Video Solution
Each of the nine words in the sentence $\text{"The quick brown fox jumps over the lazy dog”}$ is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The $\text{expected}$ length of the word drawn is _____________. (The answer should be rounded to one decimal place.)
asked
Apr 19
in
Probability
by
admin
(
3.6k
points)

1
view
gate20142
probability
expectation
numericalanswers
easy
videosolution
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