Consider the file "Google.csv" that contains daily returns of Google in 2018. Assume now that you are interested in modeling random variable X, the number of days that the Google stock will be down before it goes up (note that we can assume that a stock going down would potentially include staying the same). You can use R in all cases for probability computations, but in so doing please write down the corresponding R statements for the computations.

(a) What is the probability that the Google stock will be down more than 2 days before it goes up?

(b) What is the probability that the Google stock will be down at most 5 days before it goes up?

(c) Compute the mean and the standard deviation of the number of days the Google stock will be down before it goes up.

(d) Plot the estimated probability distribution X.

Google 0.006598587 -0.017590357 -0.001595391 -0.005733225 0.021208237 0.002318155 -0.006036625 -0.006820454 -0.002547012 0.008210051 0.008421058 0.012303535 -0.003402286 -0.011040043 0.000573608 0.008354382 -0.008927394 0.00199701 0.00356205 0.004003568 -0.010847604 -0.005148253 -0.005923273 0.007647201 0.011399775 1.05642E-05 -0.004527442 -0.009520154 0.003371542 0.023969823 0.005115089 0.009234951 -0.006418683 0.004765053 -0.005452214 0.019042567 0.008577039 -0.00133853 -0.004544961 0.018070496 0 0.002207499 0.001468425 0.001634739 0.001721058 -0.010762844 0.003224048 -0.019431511 0.002993295 0.003004615 -4.03839E-05 0.042615704 -0.000522448 -8.7081E-05 0.009254179 0.000354877 0.006730797 -0.00696191 0.009312503 0.005606309 -0.009987874 -0.003407348 -0.002825334 0.000422651 -0.00502091 0.01163626 -0.011998394 -0.001187366 0.015116091 0.001542412 0.004372933 0.014661331 -0.008134225 -0.024367795 -0.001166362 -0.010712622 -0.012877122 0.007639303 0.012867787 0.011474529 0.004604822 0.002468092 -0.003041865 0.00249816 0.005782779 0.01374037 0.012210789 -0.004893545 -0.005760405 -0.002524389 -0.001858328 -0.002816093 -0.005300957 -0.004008678 -0.002414818 0.018805712 0.017061022 0.003884482 0.013260229 0.003530539 -0.001274376 -0.002381423 0.001720534 0.016725843 4.41578E-05 0.007429049 -0.002747788 0.006628722 0.018067367 0.01031646 -0.004149064 0.00926327 0.004584943 -0.000909494 -0.007678162 0.00411933 -0.0005329 -0.052801747 -0.050759416 0.020745714 -0.026760619 -0.045195716 0.038264974 0.007923422 -0.000398312 0.017606709 0.01739539 0.003793446 0.007384725 0.009206349 -0.003456769 0.016388811 0.013837536 -0.022899311 -0.012160934 -0.029449606 0.011881521 0.009795778 0.005608548 0.01284405 0.012860494 0.027855957 0.004384832 -0.022316965 0.007877798 0.001497071 -0.014070746 -0.030279876 -0.003881478 -0.00164268 -0.037340015 -0.025257536 0.026827642 -0.044730493 -0.001747879 0.031795322 -0.023632306 0.00597453 0.010827707 0.002845514 -0.02197281 0.010040116 0.016086789 -0.011037087 0.011930989 -0.001205063 0.009709989 0.031794293 -0.003678078 0.013074267 -0.011134064 -0.00325798 -0.047652789 0.000342227 0.019863409 -0.011367769 -0.012477517 0.021765578 -0.014124382 0.000243653 0.024066988 0.00804944 -0.000821168 0.028679646 0.015170596 -0.001890568 0.002918279 -0.019636708 -0.000719007 -0.002610444 -0.010746717 0.013434422 -0.008025711 0.009904029 -0.00046964 -0.001262145 -0.014768293 0.008800945 0.020910122 0.031818182 0.015894307 -0.001751907 -0.003536054 -0.010924546 -0.001507451 0.007230503 0.006389619 -0.003448873 0.013878333 -0.000724039 0.020970038 -0.004131546 0.004564394 -0.012355693 -0.000128183 -0.025665155 -0.005845827 -0.013844055 0.008809863 0.00213876 0.01144187 -0.022615997 0.022404781 0.012082745 0.010562103 -0.000119949 0.003701309 0.025438385 0.0026306 -0.006567504 0.013848564 -0.000140075 -0.011385888 -0.001017406 0.010952679 0.038934784 0.014139742 0.007492562 -0.02536755 -0.018237815 -0.002292664 0.004701699 0.00660185 -0.002392957 -0.00039574 0.014680748 0.004371568 0.002481512 -0.009450636 -0.003089792 0.007608278