Read three variables from the Bumpus data set, which is available in the Data folder. Creatively, show plots of pairs of variables and a 3D visualization.

sex,surv,totlen,wingext,wgt,head,humer,femur,tibio,skull,stern

male,alive,154,241,24.5,31.2,0.687,0.668,1.022,0.587,0.83

male,alive,160,252,26.9,30.8,0.736,0.709,1.18,0.602,0.841

male,alive,155,243,26.9,30.6,0.733,0.704,1.151,0.602,0.846

male,alive,154,245,24.3,31.7,0.741,0.688,1.146,0.584,0.839

male,alive,156,247,24.1,31.5,0.715,0.706,1.129,0.575,0.821

male,alive,161,253,26.5,31.8,0.78,0.743,1.144,0.607,0.893

male,alive,157,251,24.6,31.1,0.741,0.736,1.153,0.61,0.862

male,alive,159,247,24.2,31.4,0.728,0.718,1.126,0.609,0.793

male,alive,158,247,23.6,29.8,0.703,0.673,1.079,0.602,0.82

male,alive,158,252,26.2,32,0.749,0.739,1.153,0.614,0.857

male,alive,160,252,26.2,32,0.741,0.723,1.129,0.624,0.892

male,alive,162,253,24.8,32.3,0.766,0.752,1.134,0.633,0.923

male,alive,161,243,25.4,31.8,0.721,0.722,1.126,0.597,0.891

male,alive,160,250,23.7,29.8,0.73,0.703,1.103,0.59,0.82

male,alive,159,247,25.7,31.4,0.729,0.717,1.141,0.592,0.927

male,alive,158,253,25.7,31.9,0.743,0.699,1.15,0.6,0.86

male,alive,159,247,26.5,31.6,0.733,0.714,1.155,0.611,0.923

male,alive,166,253,26.7,32.5,0.767,0.765,1.23,0.6,0.878

male,alive,159,247,23.9,31.4,0.752,0.723,1.113,0.602,0.825

male,alive,160,248,24.7,31.3,0.752,0.737,1.176,0.603,0.803

male,alive,161,252,28,31.8,0.77,0.731,1.19,0.59,0.885

male,alive,163,251,27.9,31.9,0.769,0.745,1.168,0.622,0.86

male,alive,156,242,25.9,32,0.723,0.711,1.116,0.609,0.886

male,alive,165,251,25.7,32.2,0.751,0.742,1.161,0.613,0.865

male,alive,160,247,26.6,32.4,0.728,0.707,1.108,0.59,0.836

male,alive,158,244,23.2,31.6,0.73,0.713,1.142,0.585,0.888

male,alive,160,242,25.7,31.6,0.709,0.705,1.124,0.62,0.788

male,alive,157,245,26.3,32.2,0.741,0.726,1.143,0.595,0.85

male,alive,159,244,24.3,31.5,0.723,0.698,1.107,0.615,0.847

male,alive,160,253,26.7,32.1,0.739,0.714,1.117,0.592,0.864

male,alive,158,245,24.9,31.4,0.726,0.703,1.119,0.58,0.854

male,alive,161,247,23.8,31.4,0.735,0.694,1.101,0.602,0.789

male,alive,160,247,25.6,32.3,0.756,0.745,1.135,0.607,0.902

male,alive,160,247,27,32,0.755,0.736,1.174,0.631,0.873

male,alive,153,241,24.7,32.2,0.728,0.68,1.092,0.592,0.884

male,dead,165,249,26.5,31,0.738,0.701,1.095,0.606,0.847

male,dead,160,245,26.1,32,0.736,0.709,1.109,0.611,0.842

male,dead,161,249,25.6,32.3,0.743,0.718,1.128,0.602,0.828

male,dead,162,246,25.9,32.3,0.738,0.709,1.135,0.607,0.869

male,dead,163,250,25.5,32.5,0.752,0.731,1.197,0.623,0.888

male,dead,162,247,27.6,31.8,0.731,0.719,1.113,0.597,0.869

male,dead,163,246,25.8,31.4,0.689,0.662,1.073,0.604,0.836

male,dead,161,246,24.9,30.5,0.739,0.726,1.138,0.58,0.803

male,dead,160,242,26,31,0.745,0.713,1.105,0.6,0.803

male,dead,162,246,26.5,31.5,0.72,0.696,1.092,0.606,0.809

male,dead,160,249,26,31.4,0.726,0.689,1.097,0.602,0.85

male,dead,161,250,27.1,31.6,0.737,0.711,1.12,0.631,0.852

male,dead,162,248,25.1,31.9,0.744,0.722,1.154,0.591,0.839

male,dead,165,252,26,32.3,0.726,0.71,1.145,0.609,0.887

male,dead,161,243,25.6,32.5,0.709,0.707,1.122,0.607,0.832

male,dead,161,244,25,31.3,0.702,0.685,1.082,0.595,0.874

male,dead,162,248,24.6,31,0.713,0.7,1.086,0.59,0.837

male,dead,164,244,25,31.2,0.703,0.69,1.074,0.608,0.795

male,dead,158,247,26,32,0.729,0.71,1.145,0.607,0.803

male,dead,162,253,28.3,31.8,0.752,0.718,1.152,0.6,0.857

male,dead,156,239,24.6,30.5,0.659,0.658,1.042,0.57,0.81

male,dead,166,251,27.5,31.5,0.72,0.691,1.118,0.612,0.847

male,dead,165,253,31,32.4,0.765,0.75,1.183,0.613,0.905

male,dead,166,250,28.3,32.4,0.754,0.718,1.179,0.607,0.916

male,alive,156,246,24.6,32,0.741,0.735,1.167,0.592,0.849

male,alive,156,245,25.5,32.1,0.761,0.717,1.147,0.62,0.816

male,alive,163,248,24.8,32.2,0.742,0.733,1.165,0.606,0.854

male,alive,163,248,26.3,33,0.736,0.704,1.148,0.609,0.839

male,alive,160,250,24.4,31.5,0.746,0.715,1.173,0.604,0.893

male,alive,156,237,23.3,30.6,0.692,0.664,1.011,0.588,0.774

male,alive,162,253,26.7,32,0.759,0.734,1.197,0.63,0.878

male,alive,163,254,26.4,32,0.766,0.75,1.165,0.605,0.886

male,alive,164,251,26.9,32,0.755,0.742,1.171,0.62,0.886

male,alive,163,244,24.3,31.3,0.718,0.68,1.082,0.61,0.892

male,alive,160,247,27,31.5,0.764,0.732,1.177,0.617,0.846

male,alive,160,250,26.8,32.5,0.764,0.729,1.123,0.635,0.842

male,alive,158,247,24.9,32.4,0.745,0.724,1.139,0.588,0.865

male,alive,158,249,26.1,32.2,0.742,0.736,1.148,0.602,0.817

male,alive,158,243,26.6,32.4,0.747,0.711,1.163,0.612,0.891

male,alive,155,237,23.3,30.2,0.685,0.653,1.011,0.587,0.794

male,dead,160,249,24.2,30.4,0.74,0.717,1.13,0.62,0.84

male,dead,156,236,26.8,30,0.69,0.671,1.067,0.563,0.832

male,dead,158,240,23.5,31,0.715,0.702,1.113,0.595,0.805

male,dead,166,245,26.9,31.7,0.715,0.695,1.107,0.601,0.847

male,dead,165,255,28.6,31.5,0.766,0.744,1.175,0.613,0.854

male,dead,157,238,24.7,31.2,0.68,0.677,1.156,0.599,0.769

male,dead,164,250,27.3,31.8,0.764,0.726,1.171,0.588,0.86

male,dead,166,256,25.7,31.7,0.752,0.751,1.187,0.595,0.858

male,dead,167,255,29,32.2,0.765,0.745,1.197,0.638,0.855

male,dead,161,246,25,31.5,0.739,0.707,1.123,0.587,0.85

male,dead,166,254,27.5,31.4,0.76,0.742,1.124,0.604,0.914

male,dead,161,251,26,31.5,0.731,0.707,1.122,0.589,0.828

female,alive,156,245,25.3,31.6,0.729,0.71,1.152,0.62,0.809

female,alive,154,240,22.6,30.4,0.705,0.686,1.103,0.584,0.77

female,alive,153,240,25.1,31,0.724,0.713,1.123,0.585,0.812

female,alive,153,236,23.2,30.9,0.698,0.678,1.132,0.596,0.795

female,alive,155,243,24.4,31.5,0.734,0.736,1.17,0.596,0.801

female,alive,163,247,25.1,32,0.748,0.734,1.166,0.602,0.821

female,alive,157,238,24.6,30.9,0.726,0.727,1.175,0.588,0.797

female,alive,155,239,24,32.8,0.732,0.742,1.175,0.601,0.835

female,alive,164,248,24.2,32.7,0.752,0.752,1.201,0.604,0.83

female,alive,158,238,24.9,31,0.741,0.689,1.091,0.592,0.866

female,alive,158,240,24.1,31.3,0.733,0.706,1.107,0.591,0.867

female,alive,160,244,24,31.1,0.731,0.73,1.152,0.589,0.808

female,alive,161,246,26,32.3,0.758,0.732,1.154,0.623,0.859

female,alive,157,245,24.9,32,0.752,0.74,1.186,0.593,0.787

female,alive,157,235,25.5,31.5,0.712,0.704,1.132,0.611,0.781

female,alive,156,237,23.4,30.9,0.708,0.691,1.123,0.613,0.798

female,alive,158,244,25.9,31.4,0.729,0.705,1.146,0.597,0.851

female,alive,153,238,24.2,30.5,0.715,0.707,1.116,0.595,0.821

female,alive,155,236,24.2,30.3,0.727,0.705,1.12,0.585,0.79

female,alive,163,246,27.4,32.5,0.732,0.711,1.163,0.63,0.862

female,alive,159,236,24,31.5,0.709,0.713,1.129,0.607,0.845

female,dead,155,240,26.3,31.4,0.709,0.71,1.125,0.614,0.815

female,dead,156,240,25.8,31.5,0.715,0.678,1.127,0.597,0.812

female,dead,160,242,26,32.6,0.71,0.732,1.157,0.597,0.854

female,dead,152,232,23.2,30.3,0.676,0.683,1.048,0.59,0.78

female,dead,160,250,26.5,31.7,0.741,0.731,1.187,0.615,0.886

female,dead,155,237,24.2,31,0.727,0.723,1.118,0.61,0.787

female,dead,157,245,26.9,32.2,0.766,0.751,1.227,0.62,0.841

female,dead,165,245,27.7,33.1,0.78,0.757,1.195,0.633,0.895

female,dead,153,231,23.9,30.1,0.68,0.662,1.042,0.592,0.781

female,dead,162,239,26.1,30.3,0.709,0.685,1.092,0.587,0.911

female,dead,162,243,24.6,31.6,0.741,0.729,1.162,0.605,0.84

female,dead,159,245,23.6,31.8,0.727,0.7,1.129,0.61,0.855

female,dead,159,247,26,30.9,0.711,0.666,1.098,0.58,0.749

female,dead,155,243,25,30.9,0.73,0.711,1.127,0.598,0.839

female,dead,162,252,24.8,31.9,0.752,0.738,1.18,0.615,0.875

female,dead,152,230,22.8,30.4,0.682,0.664,1.042,0.551,0.734

female,dead,159,242,24.8,30.8,0.717,0.667,1.09,0.575,0.809

female,dead,155,238,24.6,31.2,0.706,0.702,1.102,0.588,0.758

female,dead,163,249,30.5,33.4,0.767,0.767,1.207,0.64,0.896

female,dead,163,242,24.8,31,0.713,0.713,1.128,0.607,0.813

female,dead,156,237,23.9,31.7,0.718,0.716,1.09,0.611,0.8

female,dead,159,238,24.7,31.5,0.726,0.701,1.145,0.6,0.8

female,dead,161,245,26.9,32.1,0.751,0.704,1.142,0.607,0.819

female,dead,155,235,22.6,30.7,0.695,0.692,1.119,0.584,0.771

female,dead,162,247,26.1,31.9,0.751,0.735,1.157,0.618,0.802

female,dead,153,237,24.8,30.6,0.732,0.718,1.172,0.594,0.802

female,dead,162,245,26.2,32.5,0.728,0.731,1.102,0.614,0.832

female,dead,164,248,26.1,32.3,0.739,0.707,1.159,0.592,0.823
 

1. Verify how the Central Limit Theorem explains the standardized sum to two random variables with Uniform distribution. Notice that you must compute the correct mean and variance of the sum. How does the density of a standard Gaussian random variable fit the histogram? Show and analyze the quantile-quantile plot of these data.