Consider the daily returns of Google in 2018 listed below. Assume now that you are interested in modeling random variable X, the number of days that the Google stock will be up before it goes down three times (note that we can assume that a stock going down would potentially include staying the same). 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 up more than 2 days before it goes down 3 times?

(b) What is the probability that the Google stock will be up at most 7 days before it goes down 3 times?

(c) Compute the mean and the standard deviation of the number of days the Google stock will be up before it goes down 3 times.

(d) Plot the estimated probability distribution X.

Google

0.00659859

-0.0175904

-0.0015954

-0.0057332

0.02120824

0.00231816

-0.0060366

-0.0068205

-0.002547

0.00821005

0.00842106

0.01230354

-0.0034023

-0.01104

0.00057361

0.00835438

-0.0089274

0.00199701

0.00356205

0.00400357

-0.0108476

-0.0051483

-0.0059233

0.0076472

0.01139978

1.06E-05

-0.0045274

-0.0095202

0.00337154

0.02396982

0.00511509

0.00923495

-0.0064187

0.00476505

-0.0054522

0.01904257

0.00857704

-0.0013385

-0.004545

0.0180705

0

0.0022075

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0.00163474

0.00172106

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0.00322405

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0.0029933

0.00300462

-4.04E-05

0.0426157

-0.0005224

-8.71E-05

0.00925418

0.00035488

0.0067308

-0.0069619

0.0093125

0.00560631

-0.0099879

-0.0034073

-0.0028253

0.00042265

-0.0050209

0.01163626

-0.0119984

-0.0011874

0.01511609

0.00154241

0.00437293

0.01466133

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0.0076393

0.01286779

0.01147453

0.00460482

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0.00249816

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0.01374037

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-0.0028161

-0.005301

-0.0040087

-0.0024148

0.01880571

0.01706102

0.00388448

0.01326023

0.00353054

-0.0012744

-0.0023814

0.00172053

0.01672584

4.42E-05

0.00742905

-0.0027478

0.00662872

0.01806737

0.01031646

-0.0041491

0.00926327

0.00458494

-0.0009095

-0.0076782

0.00411933

-0.0005329

-0.0528017

-0.0507594

0.02074571

-0.0267606

-0.0451957

0.03826497

0.00792342

-0.0003983

0.01760671

0.01739539

0.00379345

0.00738473

0.00920635

-0.0034568

0.01638881

0.01383754

-0.0228993

-0.0121609

-0.0294496

0.01188152

0.00979578

0.00560855

0.01284405

0.01286049

0.02785596

0.00438483

-0.022317

0.0078778

0.00149707

-0.0140707

-0.0302799

-0.0038815

-0.0016427

-0.03734

-0.0252575

0.02682764

-0.0447305

-0.0017479

0.03179532

-0.0236323

0.00597453

0.01082771

0.00284551

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0.01004012

0.01608679

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0.01193099

-0.0012051

0.00970999

0.03179429

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0.01307427

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0.00034223

0.01986341

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0.02176558

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0.00024365

0.02406699

0.00804944

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0.02867965

0.0151706

-0.0018906

0.00291828

-0.0196367

-0.000719

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0.01343442

-0.0080257

0.00990403

-0.0004696

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-0.0147683

0.00880095

0.02091012

0.03181818

0.01589431

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0.0072305

0.00638962

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0.01387833

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0.02097004

-0.0041315

0.00456439

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-0.0001282

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-0.0058458

-0.0138441

0.00880986

0.00213876

0.01144187

-0.022616

0.02240478

0.01208275

0.0105621

-0.0001199

0.00370131

0.02543839

0.0026306

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0.01384856

-0.0001401

-0.0113859

-0.0010174

0.01095268

0.03893478

0.01413974

0.00749256

-0.0253676

-0.0182378

-0.0022927

0.0047017

0.00660185

-0.002393

-0.0003957

0.01468075

0.00437157

0.00248151

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0.00760828