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a random variable x takes the values 0

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**Design and Analysis of Algorithms Subject Code : 10CSL47 Lab Manual PROGRAM-1**

**Design and Analysis of Algorithms Subject Code : 10CSL47 Lab Manual PROGRAM-2**

**STOCHASTIC MODELS AND APPLICATIONS 10CS665**

**Econ 500: Quantitative Methods in Economic Analysis I iowa**

**Object oriented programming with c++[10CS36] unit-2**

**Saturn in Seccond House**

**DATABASE MANAGEMENT SYSTEMS LABORATORY [10CSL57] VTU prg-5**

**DATABASE MANAGEMENT SYSTEMS LABORATORY [10CSL57] VTU prg-3**

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**System stimulation and modeling [10mca52] question Bank**

**Questions**

**Consider a random variable X that takes values +1 and −1 with probability 0.5 each. -gate-cse-2012**

1 Answer

**A random variable X takes values −1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise N is independent of X, and is uniformly distributed over the interval [−2 , 2]. The receiver makes a decision X̂ = { −1, if Y ≤ θ +1, ifY > θ where the threshold θ ∈ [−1,1] is chosen so as to minimize the probability of error Pr[X̂ ≠ X]. The minimum probability of error, rounded off to 1 decimal place, is ___________.**

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**Let X be a binomial random variable with mean 1 and variance 3/4 . The probability that X takes the value 3 is**

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**Consider the random process X(t)= U +Vt, where U is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2.**

1 Answer

**If a variable takes values 0, 1, 2, 3, ......., n with frequencies 1, C(n, 1), C(n, 2), C(n, 3),......, C(n, n) respectively, then the arithmetic mean is**

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**For a discrete random variable X,ran(X)={0,1,2,3}and the cumulative probability F(X) is-gate biotech 2015**

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**If the difference between expectation of the square of a random variable (E[X²]) and the square of the expectation of the random variable (E[X])² is denoted by R, then? -gate-cse-2011**

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**If the random variable X has a poisson distribution with mean 5 then the expectation E[(X+2)2] equals**

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**If the random variable X has a poisson distribution with mean 5 then the expectation E[(X+2)2] equals**

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**The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is**

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**The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is**

1 Answer

**Let X be the Poisson random variable with parameter λ = 1. Then, the probability P(2 ≤ X ≤ 4) equals**

0 Answer

**Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by:**

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**If a continuous random variable has the following probability density function f(x) = { kx 3 , 0 ≤ x ≤ 1, 0, otherwise; then the value of k is _______________**

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**Let X be a random variable with characteristic function φX(⋅) such that φX(2 π) = 1. Let Z denote the set of integers. Then P(X ∈ Z) is equal to ...**

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**The random variable X has a probability distribution P(X) of the following form, where ‘k’ is some number.**

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**Q.11) Let X be a Gaussian random variable with mean 0 and variance σ2. Let Y = max(X,0) where max(a,b) is the maximum of a and b. The median of Y is _____. -gate computer science 2017**

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**Consider the following probability mass function (p.m.f.) of a random variable X: - gate civil 2017**

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**A random variable has the following point distribution**

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**Fill in the blanks: GATE-Computer-Science-Engineering-2017**

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