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- The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/pV:59)Q.No.6.a. A discrete variable ‘X’ has the following probability distributionX -4 -1 1 4 6P(X=x) 0.1 0.4 k 2k 0.2i. Find the value of k.ii. P (x=3)iii. P(x≥1)iv. P(-1≤X<5)b. A bag contains 5 blue and 4 red balls, choose 5 balls randomly, if ‘X’ is the number ofblue balls selected.
- I. TRUE OR FALSE. Choose A if the statement is always true, otherwise choose B. 1. The sum of the probabilities of all values of the random variable must be equal to 1. 2. The capacity of water dams in a region is an example of continuous random variable. 3. The formula u = is used to compute for the mean of a probability distribution. IxF(x) 4. A standard normal curve is a normal probability distribution that has a mean of one and standard deviation of one 5. The width of the curve in normal distribution is determined by the mean of the distribution. 6. The mean of the sampling distribution of the sample means is less than the population mean. 7. The standard error of the mean is the standard deviation of the sampling distribution of the sample means. 8. The sampling variability of the sample means becomes smaller as the sample size n gets larger. 9. In estimating the mean, the degrees of freedom is equal to (n - 1) when using the t- distribution. 10. The t-distribution is asymmetric…P(-0.34q123 The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in 90.5 = f(y) = 2 25 -Y, 0 ≤ y ≤ 5, elsewhere. 0,λ = 100 for a Y random variable with a Poisson distribution. Find the probability that the Y random variable is between 96 and 112 using the Normal approximation of the Poisson distribution.Consider the distribution of a discrete variable Y whose cumulative distribution function is given by 0, y < 12 12 ≤ y < 32 32 ≤ y ≤ 48 1, 48 ≤ y Enter below the variance of this distribution. F(y) 0.151, 0.699,
