Suppose you play a game that you can only either win or lose. The probability that you win any game is 65%, and the probability that you lose is 35%. Each game you play is independent. Let X is the number of wins If you play the game 20 times.  Find the variance of X

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The range of the random variable X is {30, 1, 2, 3, a} , where a is unknown. If each value is equally likely and the mean of X is 6, determine a. Find the variance of X

Calculate the variance of 13, 25, and 16, using the sum of squares formula (also known as the shortcut formula) for sample variance, where x represents the data value and n is the number of values. (E x)* Ex? variance = п — 1 Step 1. Determine the sum of squares of the three values. Ex = Step 2. Determine the square of the sum of the three values. (Ex)° = Step 3. Divide the result in Step 2 by n. (Ex)² Step 4. Subtřact the result in Step 3 from the result in Step 1. (Ex) Ex? - n Step 5. Divide the result in Step 4 by n – 1. Ex? - (Ex)? п — 1