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Consider the following two lotterics: L $200 with probability 0.7, 0 with probability 0.3, and L'...
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Consider the following cumulative distribution function for X. 7 0.1 08 0.9 1.0 Fo) 0.3 0.6 (i) Determine the probability distribution. ii) Find P(X < 1). iii Find P(0 <XS5).
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
I need this equation's analytical solution with this
non-homogenous boundary conditions
=07 , 0 x L,120 where a = 0.013 L=1 Initial condition T(z,0) = 0 BCs are 70, t > 0) = 50 TL,t50
4. Consider the probability density function (x)for x>0, and zero otherwise. Determine a. The value of a b. P(X> 22) C. e The value of x such that P(X<x)-0.1
(1 point) A random variable with probability density function p(x; 0) = 0x0–1 for 0 <x< 1 with unknown parameter 0 > 0 is sampled three times, yielding the values 0.64,0.65,0.54. Find each of the following. (Write theta for 0.) (a) The likelihood function L(0) = d (b) The derivative of the log-likelihood function [ln L(O)] = dᎾ (c) The maximum likelihood estimate for O is is Ô =
The Pareto probability distribution has many applications in economics, biology, and physics. Let β> 0 and δ> 0 be the population parameters, and let XI, X2, , Xn be a random sample from the distribution with probability density function zero otherwise. Suppose B is known Recall: a method of moments estimator of δ is δ = the maximum likelihood estimator of δ is δ In In X-in β has an Exponential (0--) distribution Suppose S is known Recall Fx(x) =...
The random variable X and Y have the following joint probability mass function: P(x,y) 23 0.2 0.1 0.03 0.1 0.27 0 4 0.05 0.15 0.1 a) Determine the marginal pmf for X and Y. b) Find P(X - Y> 2). c) Find P(X S3|Y20) e Determine E(X) and E(Y). f)Are X and Y independent?
2) Consider a random variable with the following probability distribution: P(X-0)-0., Px-1)-0.2, PX-2)-0.3, PX-3) -0.3, and PX-4)-0.1 A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated values. How do these summary measures compare to the...