The density function of a continuous random variable X is shown below. Find (a) the mode. (b) the median, and (c) the mean. -x(1-x²) -0.4 ≤x≤1 f(x) = (2500 441 otherwise
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- X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 1/4 of the expectation of X (ie Var(X)=0.25E(X)). The probability that X is greater than 7 is equal to_____. Please fill in the blank.Example . Let the random variable X of the continuous type have the p.d.f. Ax) = 2/x, 1 < x< 0, zero elsewhere. The distribution function of X is %3DFind the standard deviation. (Enter an exact number as an integer, fraction, or decimal.) x P(x) x*P(x) (x − ?)2P(x) 2 0.1 2(0.1) = 0.2 (2 − 5.4)2(0.1) = 1.156 4 0.3 4(0.3) = 1.2 (4 − 5.4)2(0.3) = 0.588 6 0.4 6(0.4) = 2.4 (6 − 5.4)2(0.4) = 0.144 8 0.2 8(0.2) = 1.6 (8 − 5.4)2(0.2) = 1.352
- Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1A random variable X has the cumulative distribution function as below.Calculate the variance of X.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)Find the standard deviation. Р(x) | x*Р(x) (x - 4)°P(x) 2 0.1 2(0.1) = 0.2 4 0.3 4(0.3) = 1.2 6 0.4 6(0.4) = 2.4 8 0.2 8(0.2) = 1.6 00Find the expectation. Find the variance. Find The CDF. Find P {X = 1/5 }. Find P { 1/8 ≤ X ≤ 3/8 }.Continuous random variables 6. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Find the Expected value and Standard deviation.Express your answer in 3 decimal place value f(x)= - c(x-1)(4-x) 0 for 1min {X1, X2}. %3D Suppose that X1, X2 are iid, and X1 Exp(2). Find the distribution of X(1)X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 3/4 of the expectation of X (ie Var(X)=0.75E(X)). The probability that X is less than 2 is equal to_____. Please fill in the blank.Let X be a random variable with p.d.f f(x) =x(9-x),0 sI5 3. Find the mode.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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