The cumulative distribution function for a random variable X is given by: 1-e for x20 F(x)=- otherwise Compute P(3< X < 4)

Q: Determine the value of c such that f(x) = (c / x2) for x > 1 represents the p.d.f. of a random…

A: Given that  f(x)=c/x2   , x&gt;1

Q: Let the probability function of the random variable X be defined as f(x)=1/(2(1+∣x∣)²). Draw the…

A: From the given information, Consider, the pdf: f(x)=1/(2(1+∣x∣)²) fx={ 121+x2, x≥0      ={121-x2,…

Q: 1- P(Y > 1) 2- P(X>2|Y< -1) 3- P (3<X<7)

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Q: The probability distribution of X is given as: f(x) = { 0.4; x = 1 (x-1)/4; 1 < x < 2 (3-x)/4; 2…

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Q: The cumulative dietribution function for a random variable X ie given by: (1-e* F(x)={ for x20…

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Q: (i) Find the mean of X (ii) Find the variance of X

A: Given,(i)we calculate the mean of let's calculate the mean:Here we have findoutThe

Q: Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that…

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Q: Let X be a random variable with expectation E(X)=10 and variance var(X)=5. Which lower bound does…

A: Let 'X' be the any non-negative random variable having mean E(X) and Variance Var(X) then…

Q: Let X denote the number of VCRs sold during a random week by a certain store. The probability…

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Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: When mean number μ of Atlantic hurricanes per year is given: μ=6 Find the probability that in a…

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Q: Let F(z) be the cumulative distribution function (cdf) of a random variable X. Which of the…

A: Based on the property of cumulative distribution, P(a&lt;X&lt;b) = F(b) - F(a) F(a) + P(a&lt;X&lt;b)…

Q: The waiting time, in hours, between successive speeders spotted by a adar unit is a continuous…

A: Solution

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: We want find  Mean= E(x) , variance = var(x)

Q: A random variable X has a normal distribution N(4,9). (1) Find V(X) and E(X²). (2) Let + be the cdf…

A: The normal distribution of the random variable is N(4,9).

Q: be able wopue. əui un variance Var(X). Then the standard deviation o x of X is defined by Select…

A: We want to tell Let X be a finite random variable with the variance Var (X). Then the standard…

Q: If a random variable that follows exponential distribution shows that P(X2000)=0.7, Then P(30002000)…

A: Exponential probability distribution has memoryless property i.e. P(X &lt; a   | X &gt; b) = P(X…

Q: probability Find the mean of x. vailable is P(x) = (3Cx)(¹/4)*(3/4)³* for x = 0,1,2,3

A: It is given that the probability distribution of discrete random variable X follows Binomial…

Q: The cumulative distribution function for a random variable X is given by: for x20 F(x)= otherwise…

A: Now calculate probability value between 3 to 4.  So, use the formula is, FXx=PX≤x…

Q: x is a uniform random variable in the interval (x1,x2). Find the expected value of x

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Q: A random variable X has P(5<X<19) 2 0.75. Using Chebyshev's theorem, the mean and variance (H, o2)…

A: The mean will be the average of 5 and 19. So, mean= (5+19)/2=12

Q: A fair 6-sided die is tossed. If X denotes the random variable giving the number on the bottom face…

A: The sample space of 6-sided die tossed is {1,2,3,4,5,6}. It is given that X denotes the random…

Q: Suppose that a pair of fair dice are to be tossed, and let the random variableX denote the sum of…

A: A pair of fair dice to be tossed.The possible outcomes are 62 = 36The sample space is,S={ (1, 1),…

Q: Let X denote a random variable that has a Poisson distribution with mean 1= 2. Find (a) P(X = 4) %3D…

A: Here X~ Poisson with parameter 2. We need to find the required probabilities.

Q: x < 0 0 < x < 1 F (x) 3x 2 1

A: Let x be the Continuous random variable having cumulative distribution function F(x)

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii. Var(X)…

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Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: A random variable X has the cumulative distribution function. Calculate the Expected Value of X…

A: Answer: - Given, the CDF of X is                 F(x)   x2-2x+221≤x&lt;21x≥2                    Find…

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find:    i. E(X) ii.…

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Q: 4 f(x) = OTHERWİSE 0, -12112

A: EX=∫-20x.fxdx+∫02x.fxdx=∫-20x12+x4dx+∫02x12-x4dx=∫-20x2+x24dx+∫02x2-x24dx=12∫-20xdx+14∫-20x2dx+12∫02…

Q: If E denotes the expectation (random variable X is denoted the variance of a as (E(X))^2 - E(X False…

A: Given,E denotes the expectation .

Q: A student takes a test in which they have to indicate whether each of n statements is true or false.…

A: It is interpreted that each statement has the only option of being "correct" (defined as success) or…

Q: X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 1/4…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!