Random variable X has a continous probbabilty distribution defined by distribution function: (picture) Determine the distribution function and marginal density of random variable Y=X2
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Random variable X has a continous probbabilty distribution defined by distribution
- Determine the distribution function and marginal density of random variable Y=X2
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- Please be specific.The probability density function of a random variable is kVx+ – 1 f(x) if 1< x< 2 = 0 otherwise Find the k. The marks obtained in mathematics by 1000 students are normally distributed with mean 78% and standard deviation 11%. Determine what was the highest mark obtaianed by the lowest 10% of the student? oninte The probability density function of a random variable is kx³ f(x) if 0sx<2 V25 – x² = 0 otherwise Find the k.1 example solution of mean and variance using Hypergeometric Distribution.
- OmarA random variable is normally distributed with a mean of μ = 50 and a standard deviation of a = 10. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 20 and 80). Areas Under the Curve for any Normal Distribution O O м-30 20 μ-20 30 40 20 40 60 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 20, 30, 40, 50, 60, 70, and 80. 99.7% 95.4% μ-lo н 50 68.3% 60 μ + lo 70 80 A T μ + 20 80 70 50 30 +30 80 X 70 60 50 40 30 20 30 50 70 80 60 40 20 (b) What is the probability the random variable will assume a value between 20 and 80? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 40 and 60? (Round your answer to three decimal places.)Question * Given X be the life time of a bulb having a probability density function f(x) =-e for x>0 and 0 elsewhere. The mean life time of the bulbs is equal to: %3D O 1/2 O None of these O 1/4 Question* Let X and Y be two independent continuous random variables with marginal distribution
- • The value of the test statistic is given by 1= • The p-value is the area under the curve to the right of the value of the test statistic. Student's t Distribution 0,4 + Step 1: Enter the number of degrees of freedom. 17 Step 2: Select one-tailed or two-tailed. 0.3+ O One-tailed O Two-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) 0.2+ 1.928 Step 4: Shade the area represented by the p-value. 0.1+ Step 5: Enter the p-value. (Round to 3 decimal places.) 0.0354 1= 1.928 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by Ashley. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean number of cases directly generated ? by one previous case is greater than 2.6. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is…Question * Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysrsl elsewhere 3. E(X')= 3. 3. with E(X) E(Y) = 2, E(Y') = and E(XY)= 10 Then the value of the varianee of X+Y IS. 91/320 3/80 43/320 7/20Ch: Estimating Random Variables Q: The beta distribution plays an important role in Bayesian statistics. It has two parameters, called shape parameters. Let X and Y be independent uniform random variables on the interval [0,1]. Estimate via simulation the pdf of the maximum of X and Y and compare it to the pdf of a beta distribution with parameters shape1=2 and shape2=1. Use 'dbeta()'. (use R-code)
- Plot the gamma distribution by fixing the shape parameter *k* = 3 and setting the scale parameter = 0.5, 1, 2, 3, 4, 5. What is the effect of increasing the scale parameter?Time between accidents in an industrial setting are exponentially distributed with a mean of 100,000 man-hours of operation. Determine the probability that next accident will occur before 80,000 man-hours of operation. Pr(Next accident is before 80000 hrs)=