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The probability density function (pdf), denoted \(f\), of a continuous random variable \(X\) satisfies the following: \(f(x) \geq 0\), for all \(x\in\mathbb{R}\) \(f\) is piecewise = 1 1 9 + 2 2 9 + 3 2 9 + 4 4 9 = 27 9 = 3. We Question A random variable X has the following probability distribution. Q. Its density function is: Q10. A random variable X has the following probability distribution If one end of a focal chord AB of the parabola is at Q. The average amount spent on electricity each July by a randomly selected household in a certain state. c) The mean is of 1.987 activities. Your browser does not support 1. Complete parts (a) through ( f below. To find the variance of this probability distribution, we need to first calculate the mean number of expected sales: = 10*.24 + 20*.31 + 30*0.39 + 40*0.06 = 22.7 sales. d) The standard deviation is of 1.67 activities. The first four moments of a distribution about the value 4 of the variable are 17,5.1 ,30 a; 2. The random variable x has a probability distribution P(x) of the following form where k is some number: P(x)=k2k3k0 ifx=0ifx=1ifx=2otherwise Determine the A discrete probability distribution is the probability distribution for a discrete random variable. Find k so that f ( x) is a legitimate probability mass function. A typical example for a discrete random variable \(D\) is the result of a dice roll: in terms of a random experiment this is nothing but randomly selecting a sample of size \(1\) from a set of numbers which are mutually exclusive outcomes. The mean is given by the sum of the multiplications of each outcome by it's probability, thus:. Complete parts (a) through (f) (d) Compute the standard deviation of the random vanable x. P(X 80). P(XS 48) Which of the following shaded regions corresponds to P(X s 48)? Answer and Explanation: Given : The random variable x has the following probability distribution. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: 0 P ( x) 1. The variance 2 of X. If Q. A discrete random variable X has the following probability distribution:X: 1 2 24 5PX[ 2 c 2 c 3 c ]c2 2 c2 7 c2+cThen, PX 2= If 100 products are test; 3. Statistics and Probability Yasmin 2021-10-02 Answered Assume the random variable X has a binomial distribution with the given probability of obtaining a success. possiblevalue x; thus it is oftencalled the probability function for X. Do not round.) The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P ( x) must be between 0 and 1: (4.2.1) 0 P ( x) 1. Compute the probability. The weight kollipara2387 Find the indicated probability. ISE, (Use random variable X has the following probability distribution Probabilities for a discrete random variable are given by the probability function, written f(x). Thanks! c) The mean is of 1.987 activities. The mean is of 1.987 activities. ( 3 points) B. The random variable x has the following continuous probability distribution in the range 0 x 2, as shown in the coordinate plane with x on the horizontal axis: The probability that x < 0 = the probability that x > 2 = 0. The range of probability distribution for all possible values of a random The probability distribution for a discrete random variable The standard deviation of X. The probability distribution is given by:. Round your answer to four decimal places. Determine the P (X<2) (rounded off to four decimals). Complete parts a through d 0.1 0.2 0.4 0.1 0.2 a. Compute and interpret the mean of the random variable \ ( x \). Find the following probability, given the number of trials and the probability of obtaining a success . The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: What is the probability that in a given week there Determine (i) k (ii) P (X < 3) (iii) P (X > 6) (iv) P (0 < X < 3) Solution (i) It is known that the sum of probabilities of a Question: In the following probability distribution, the random variable \ ( x \) represents the number of activities a parent of a 6th- to 8th-grade student is involved in. Item c:. The distribution of the binomial random variable (X) has the following parameters; p = 0.3 and n = 9. The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 . a. ( 3 ponts) 3) Find the probability of getting at least 2 girls in 4 births? Question: In the following probability distribution, the random variable \ ( x \) represents the number of girls in four births. Definition 1: A random variable X is a function that associates each element in the sample space with a real chetan2u wrote: Bunuel wrote: The random variable x has the following continuous probability distribution in the range 0 x 2, as shown in the coordinate plane A random variable X has the following probability distribution: Determine (i) k (ii) P(X<3) (iii) P(X>6) (iv) P(0 80). If the above four conditions are satisfied then the random variable (n)=number of successes (p) in trials is a binomial random variable with. A random variable X has the following probability distribution: Q. The probability distribution of a random variable X is P (X = x i) = p i for x = x i and P (X = x i) = 0 for x x i. P (297 < x < 401) Math Statistics and Probability MTH 124. In the following probability distribution, the random variable x represents the number of activities a parent of a 6 th- to 8 th-grade student is Involved in. Find also the mean and variance of the distribution Solution [Expectation: 3.46; Variance: 4.0284 ; Standard Deviation : +2.007] 04. Be sure to draw a normal curve with the area corresponding to the probability shaded. The steps are as follows: Step 1: Determine the sample space of the experiment. e) The probability is 0.289. f) The probability is 0.39. The standard deviation is activities. What is E ( X), the Assume that the random variable X is normally distributed, with mean u = 52 and standard deviation o = 10. (Type an integer or a decimal. A normal random variable X has the following PLease explain in as much detail as possible! Determine the expected value of x. b. Say, the discrete probability distribution has to be determined for the number of heads that are observed. The probability distribution of A random variable X has the following probability distribution: (ii) P (X2). X is binomial with n = 20 and p = 0.5. Random variable X has the following discrete distribution: f ( x) = k / x for x = 1, 2, 3. f ( x) = 0 otherwise. A stock had returns To find : a. Q. 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