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The random walk model for a stock price assumes that at each time step the price...

The random walk model for a stock price assumes that at each time step the price can either increase or decrease by a fixed amount ∆ > 0. Suppose that P1, 0 < P1 < 1 is the probability of an increase and that P2 = 1−P1 is the probability of a decrease. Let X be the discrete random variable representing the change in a single step and Y be the discrete random variable representing the number of increases observed in 10 steps.

Find the variance of the random variable X.

Math   Statistics-And-Probability   
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Since variance of x alone is asked only it is calculated

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