4 Discrete e Random Variables are given. Prebbility Discrete Funden( PDE); Por ro Q1,15, 2, 25,3,35 9115,3, 25,3,35 x+1 a) Find varieble B b) Find mean and variance 2Optin the contiauous Deasity funchion (CDF)
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- Is cov(X, Y) random?In rolling a fair die once, what is theprobability of rolling a 2 or an oddnumber? show solutionThe height of male students in the school is assumed to be normally distributed. 18% of the students haveheight more than 180 cm and 9% of them have height less than 160 cm. Find µ and σ.
- Find the coefficient of skewness using Karl-Pearson's and Bowley's.The Weight and Blood Pressure of 26 Randomly Selected Male People in a Group ages 25 to 30 are shown in the following table. Suppose weight and blood pressure are normally and jointly distributed Y= 69.1044 + 0.4194x A)Test the hypothesis that rho = 0 and test the hypothesis that rho = 0.6A hexagonal cell within a seven-cell system has a radius of 1.425 km. A total of 119 channels are used within the entire system. If the load per user is 0.028 Erlangs, and λ = 1 call/hour, compute the following for an Erlang C system (chart is attached) that has a 7% probability of delayed call: B) What is the probability that a delayed call will have to wait for more than 9 sec?
- Consider a circle with random radius R ∼ Uniform(0,5). What is the probability that the area of the circle is greater than the circumference?State the conditions required for performing a Kruskal– Wallis test.A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j^2 for j = 1, 2, 3, 4, 5, 6. What is the probability of rolling at most three sixes in 5 independent casts of this die?
- Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].The probability limit of the OLS estimator in the case of omitted variables is given by the following formula: Give an intuitive explanation for two conditions under which the bias will be small.A computer disk storage device has ten concentric tracks,numbered 1, 2,…, 10 from outermost to innermost, and asingle access arm. Let pi 5 the probability that any particularrequest for data will take the arm to tracki(i 5 1,… , 10). Assume that the tracks accessed in successiveseeks are independent. Let X 5 the number of tracksover which the access arm passes during two successiverequests (excluding the track that the arm has just left, sopossible X values are x 5 0, 1, …, 9). Compute the pmfof X. [Hint: P(the arm is now on track i and X 5 j) 5P(X 5 j|arm nowon i) ? pi. After the conditionalpro bability is written in terms of p1,…, p10, by the law oftotal probability, the desired probability is obtained bysumming over i.]