(3) Five balls are randomly selected without replacement from an urn with 11 black and 10 white balls. Let X be the number of black balls selected. Compute Var (X).
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- Suppose we have an urn with a total of 10 balls where 5 balls are marked with number "1" and 5 balls are marked with number "0”. Suppose we draw two balls without replacement from the urn. Let the number on the first ball be X1 and the number on the second ball be X2. Find P(X1 >=X2). (Note: Justify all your steps.)We throw a symmetrical dice twice. Let X denote the number of throws in which an odd number of dice fell, and let Y denote the remainder of the product of the dice's rolls divided by 3.Check whether the variables X and Y are (a) independent (b) uncorrelatedA large bag contains pretzels with 3 different shapes: heart, square, circle . Billy plans to reach into the bag and draw out one pretzel at a time, stopping only when he has at least one pretzel of each type. Let the random variable X denote the number of pretzels that Billy will draw from the bag. You can assume that there is an infinite number of pretzels in the bag with equal proportions of each shape. Find E(X).