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- X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.Let X be discrete random variable. If P(XUsing the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.
- Suppose the following is a valid probability distribution. Find the value of m. 3 4 6. P(x) 0.05 0.12 0.35 0.32 Select one: a. 0.16 b. cannot be determined C. 0.08 d. 0.84 pe here to search 近Using the standard normal distribution, what is the probability that z>1.3936 ? O 0.0409 0.9183 1.8366 0.1634 0.0817In a joint probability distribution table for 4 variables (A, B, C, D), how many entries will there be? 4 8 16 32
- What is the likelihood ratio p(x|C₁) p(x|C₂) in the case of Gaussian densities?2. A discrede random varPable X has the followFny Probability distrbfution: the Value 2. 34 6 7 PO)C 2c 3C c2c4ad 20 d.Let X be a random variable with density function 1) ={0. k(1 -x), if 0<*<1; otherwise. f(x) Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1.
- Let X be a continuous random variable with probability density function = {1/³ fx (x) if -1 < x < 2 otherwise 0 Let Y = X². Find the cumulative distribution function for Y.Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ=1/10. If someone arrives immediately ahead of you at a public telephone booth, find the probability that you will have to wait, (a) More than 10 minutes (b) Between 10 and 20 minutesLet X and Y be two binary, discrete random variables with the following joint probability mass functions. (a) Compute P(X = 0]Y = 1). (b) Show that X and Y are not statistically independent. P(X = 0, y = 1) = P(X = 1, Y = 0) = 3/8 P(X = 0, y = 0) = P(X = 1, Y = 1) = 1/8