# Recent questions tagged uniform-distribution

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For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________
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Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it moves to one ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
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Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
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1 vote
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1 vote
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You arrive at bus stop some time uniformly distributed between $10:00$ and $10:15$ and bus leaves the bus stop sometime uniformly distributed between $10:00$ and $10:25$. What is the probability of you missing the bus?
1 vote
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After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (c) Assume that you know in advance ... . Let $M$ be the amount of time of the show that you miss because of th call. Compute the expected value of $M$.
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After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval (b) At $8.30$, the call still hasn't arrived. What is the probability that it arrives in the next $10$ minutes?
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After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (a) Compute the probability that the call arrives between $8.30$ and $8.20$.
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According to Universality of Uniform , We can get from the uniform distribution to the other distributions and also from other distributions back to the uniform distribution. Please explain how we would simulate from one distribution to other distribution ?
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Suppose that $X$ is chosen uniformly from $\{1,2,\ldots,100\}$ and given $X =x$, $Y$ is chosen uniformly from $\{1,2,\ldots,x\}.$Then $P(Y = 30)=$ $\dfrac{1}{100}$ $\dfrac{1}{100} \times \left(\dfrac{1}{30} + \ldots+\dfrac{1}{100}\right)$ $\dfrac{1}{30}$ $\dfrac{1}{100} \times \left(\dfrac{1}{1} + \ldots +\dfrac{1}{30}\right)$
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Assume that in a traffic junction, the cycle of traffic signal lights is 2 minutes of green(vehicle does not stop) and 3 minutes of red (vehicle stops). Consider the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time in minutes for the vehicle at the junction is _________
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The average number of donuts a nine-year old child eats per month is uniformly distributed from 0.5 to 4 donuts, inclusive. Let X= the average number of donuts a nine-year-old child eats per month. Then X~∪(0.5,4) The probability that a different nine-year-old child eats an average of more than two donuts given that his or her amount is more than 1.5 donuts is ________. 4/5 1/5 2/5 3/5
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A arrives at office at 8-10am regularly; B arrives at 9-11 am every day. Probability that one day B arrives before A? [Assume arrival time of both A and B are uniformly distributed]
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In the cartesian plane, selection of a point P along the y axis in [0,2] is uniformly random. Similarly selection of a point Q along the x axis in [0,2] also uniformly distributed. What is the probability of the area of the triangle POQ to be less than or equal to 1, where O is the origin ?
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In cartesian co-ordinate system,along the x axis two points p and q are selected uniformly at random in $\left [ 0,L \right ]$ where L > 0. What is the probability of $\text{distance(p,q)} \leq \frac{L}{4}$.
1 vote
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Question A subway train in a certain line runs after every half hour, between every midnight and 6 in the morning. What is the probability that a man entering the station at random will have to wait at least 20 minutes? I'm stuck here... It can be solved using ... ? in this case what is the upper limit of the integral ? URL : https://www.assignmentexpert.com/homework-answers/Math-Answer-40654.pdf
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Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is $1/ (2\alpha)$ exp $(1 - \alpha)$ $1 - \alpha$ $(1 - \alpha)^{2}$ $1 - \alpha^{2}$
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Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$? $3 (1 - b) a (b - a)$ $3 ((b - a) - (b^{2}- a^{2})/2)$ $6 (1 - b) a (b - a)$ $(1 - b) a (b - a)$ $6 ((b^{2}- a^{2})/ 2 - (b^{3} - a^{3})/3)$.
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Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
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Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave. What is the probability that the two will not meet?
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
A point is randomly selected with uniform probability in the $X-Y$ 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 $\left(\dfrac{2}{3}\right)$ $\quad 1$ $\left(\dfrac{4}{3}\right)$ $\left(\dfrac{5}{3}\right)$
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$