3. Given the probability function of a random variable as F(x)=1-4/x² for x> 2 and - 0 for x<= 2, where F(x) is defined

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3 Given The Probability Function Of A Random Variable As F X 1 4 X For X 2 And 0 For X 2 Where F X Is Defined 1 (52.27 KiB) Viewed 28 times

3. Given the probability function of a random variable as F(x)=1-4/x² for x> 2 and - 0 for x<= 2, where F(x) is defined as PCX<=x). Do not use R for this problem. Using this distribution function, find the probability that this random variable will take a value (1) less than 3 and (ii) x is between 4 and 5. 4. Check if the following function are valid probability distribution function for the range of x given. Use R for this program. Make sure to check the properties are satisfied, to have this function being qualified to a be a probability distribution function. The function f(x) is defined as: f(x)=P(X=x) (1) f(x)=x²/57, for x = 1, 2, 3, 4, 5 (11) f(x)=(x-3)/10, for x = 3, 4, 5, 6,