what is the value of the constant c for plx) to qualify probability mass function? plx) = d if x = 1,2,3,4, ... and pl) = 0 other wise.
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- Findi) the joint probability function of ?1and ?2.ii) the probability that less than 3 heads will occur and the student will win R1 or less.SOLVE STEP BY STEP IN DIGITAL FORMAT ÿ » Ü ¸♥ 286. Let X be a random variable with distribution Ber(p) and let a and b be two constants with a 0. Define the random variable Y = ax + b. find a) The probability function of Y. b) E(Y). c) Var(Y). d) E(Y) for n = 1, 2,...Q5 Let = {} 1 f(x) = x = 1, 2, 3, 4, 5, 6, otherwise. be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a random sample of size 5 from this distribution is 5 91 (y₁) = = (²-")" - (0 =³) "₁ 6 6 y = 1, 2, 3, 4, 5, 6. and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X₁, and X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.
- Let X equal the IQ of a randomly selected American. Assume X ~ N( μ μ {"version":"1.1","math":"μ"} =100, σ σ {"version":"1.1","math":"σ"} =4). What is the probability that a randomly selected American has an IQ below 90?3. If the probability density function of random variable is given by f(x)=1/sechx 1 ≤ x ≤ 2 a) Find the mean b) Find the total areaThe salaries of workers represent uniform distributed random variable from1000 to 2000 dollars. a) Construct corresponding probability density function. b) Find the probability, that the salary of randomly selected worker is not less than 1400 dollars.
- I have Answered Part (i) of this question but im stuck on the rest from Part (ii) - (iv) please help Q2. i) Two six-sided dice are rolled and the scores added together. Draw the sample space, the probability density function and the cumulative probability density function by hand. ii) What is the probability that the number obtained on one of the dice is a multiple of a number obtained on the other dice? What is the probability of doubles (1,1, 2,2. etc)? iii) A weekly lottery with numbers 1-49 has come up with the numbers 2,4,6,8,10 and 20,25,30,35,40 over the last month. There have been claims of fraud and the organisers are worried as ticket sales are down.Write a short paragraph on the issue giving views based on your knowledge of probability. iv) Use four letter word to explain and illustrate the differences between permutations and combinations. Give an example where the distinction between permutations and combinations is crucial.The random variable X has the geometric distribution with probability mass function (pmf) Py(x) = q*p. x = 0,1, 2, ... 0 x). |A7 The random variable X has the binomial distribution with probability mass function () p*(1 - p)²-*, x = 0, 1,2; 0b) Sketch the probability mass function and the cumulative distribution function of X (c) Consider a random sample of 6 parcels. If Y is the number of parcels taking longer than 1 day to arrive, write down the distribution of Y and its mean and variance.Assume that 1 in 300 people cany the defective gene causes ed colon cancer iha sanple of 1000 individuals approximate the probability that a) at least 10 cary the gene (three decimal places)a box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?
