In their article "A Case Study of the Use of an Experimental Designin Preventing Shorts in Nickel-Cadmium Cells" ({Journal of QualityTechnology}, 1988), Ophir, El-Gad, and Snyder describe aseries of experiments conducted in order to reduce the proportion ofcells being scrapped by a battery plant because of internal shorts. The experimental program was successful in reducing the proportion ofmanufactured cells with internal shorts to around 0.02.Consider the following experiment ...Suppose that testing of cells for internal shorts beginson a production run in this plant, Consider the random variable:X = the number of 'good' cells tested ... ... before the first cell with an internal short is discovered.[(4.a)]What are the possible values for X? Is X discrete or continuous?What is the appropriate distribution for X?What is the expected value of X, E[X], if the proportion ofmanufactured cells with internal shorts is p = 0.02?What happens to E[X] if p increases? Choose one: [Larger or Smaller]